It won't be unsafe if it were calculated. (Actually based on data.)
I think the pushback you are getting is coming from the concept of aborting past V1, however it is calculated, is a bad idea.
The problem that guys like me have with the pushback is that, yeah, sure in a jet or whatever, yeah, V1 is a hard number, but when I was in the left seat of the 1900 on a cold day looking at 10,000' of dry runway in front of me, I thought it was hilarious to take the thing flying when you have about 7500 to 8000 more feet of runway in front of you to stop in if you lose an engine in the 5kt window between V1 and Rotate. To be honest, I wouldn't even have to touch the brakes and I wouldn't go off the end. I always thought it was silly to even have V1 in that airplane, and thought it was hilarious when guys on this forum would tell me that you should "never-take-it-in-the-air-after-v1-no-matter-what!!!!1!!" To me, that kind of rigid, meat-computer type thinking doesn't have a place in professional aviation, but reading these forums sometimes one gets the impression that any critical thinking is dangerous. And while I will certainly be the first to say, "FTFM - or Follow the F-ing Manual" if one simply regurgitates the AFM without really knowing why things are the way they are, then that kind of defeats the purpose of even having a pilot there in the first place, right?
But that's the thing, there's a time and a place for everything, and if you're going to do something, be damned sure to have a reason for it. I mean, I don't fly the airplane, but I would bet you could abort a few knots after V1 in the Citation Mustang on a 10,000' sea-level runway and not have a problem, but that does put you squarely in test pilot territory - so you should have an answer for why you're aborting, and preferably one that is based on some sort of data so you can prove it.
Probability of an overrun during an abort after V1 depends on a lot of factors - to include how much energy you're dissipating with brakes versus their capacity to disperse, what kind of head wind you have, the runway slope, how rapidly the pilot acts to correct the problem, aircraft automation, and so on. In any case, you should be planning on taking an airplane flying after V1 except in very specific circumstances (a la 1900 on a 10,000' runway, or something that makes flying unreasonable).
That said.... consider this, what are some Vref speeds in these airplanes without flaps? I'd be willing to bet that they are higher than V1 in a lot of situations, and the airplane
should be able to land without flaps and not kill everyone - so, if you
really needed it to "not die" - that is to say something like the FO notices a fire in the wing after V1, or a volcano erupts in the mountains right off then end of the runway, or something else silly happens - there's certainly
some ability to abort. Indeed, I'd bet a fella could even go as far as to say that you could find some guidance aborts after V1 by looking at no-flap landing data, or something of that nature. Not that that really helps you in the heat of the moment, because who is going to look up your no-flap landing distances and speeds (if they're even published) prior to takeoff and it still doesn't tell you if you're going to be able to make it in the rare event that your airplane has any of that published...but... it
is something to think about.
I would also say that it is helpful to talk about and think about these sorts of things. I mean, there
are times where taking an airplane flying after V1 can be a bad idea - they are
exceedingly rare and probably not the sort of things we should be spending time on in training, but for hangar flying like we're doing here, they are a great tool to probe what happens when things go wrong. I mean, in part 25, they talk about waiting 2 seconds after V1 in terms of calculating accelerate stop distance - so how much extra speed does "1 potato, 2 potato" get you? 5kts? 10kts? I guess it would depend on the airplane, the situation, and so on. There's also a note in there that refers to 25.101 that says:
(i) The accelerate-stop and landing distances prescribed in §§25.109 and 25.125, respectively, must be determined with all the airplane wheel brake assemblies at the fully worn limit of their allowable wear range.
You should also be aware that:
(f) The effects of available reverse thrust—
(1) Shall not be included as an additional means of deceleration when determining the accelerate-stop distance on a dry runway;
So your brakes have to suck, and in your panic during the abort you cannot use reverse, so there is
some margin built into the system - not a lot, but some.
Also, why you're aborting matters, if you're aborting after V1 because of an engine failure - yeah, aborting after V1 is typically silly, but there are times when it could make sense - especially under part 91. Consider this scenario where you end up going to some airport up in the mountains, there's no reg that I know of in part 91 that specifies you need to be able to meet the climb gradient on departure single engine (if there is someone please call me out), and while you could depart at 7:30am like your boss wanted to, he was delayed by another meeting and pushed back departure until 2:30 when it's 100°. Now, you can make the climb gradient out of there with both engines running, but not single engine. You've got 8,000' of runway left in front of you, and you experience an engine failure at V1 +5...what do you do? The best answer is don't even try to depart but if you do decide to go fly - is it better to shoot off the end of the runway at 25kts, or impact a mountain while trying to fly an obstacle departure you can't meet the climb gradient for? I hear stories from buddies flying corporate (or even some of the charter places out there) about these sorts of situations constantly - hell, in the C90 (where we don't have a true V1) there are times where it could behoove me to accept a bent airplane and broken pride then try to take it flying if I were in the high desert somewhere. It sounds unpleasant, but these are the things you should be thinking about before you conduct operations - "wow, it's freaking hot...and my OEI climb gradient is -200fpm....hmmmm."
A situation I could see in the 135 world for aborting a takeoff after V1 is nailing a deer/moose with the wing during the departure roll after V1. It's very plausible that you could take the airplane around, land, and have it be no big deal - but if you nail a 500lb moose calf at 135kts how well will that wing hold up on your trip around the patch? The airplane may very well rotate and fly for a little while, but then what? The airplane
may still be airworthy - but you don't know for how long or how far it can go. Frankly, in that scenario, I'd probably rather take my chances shooting out into the weeds at the end of the runway at 30 or 40 knots than try to take a sick airplane on a joy-ride just because I was past a particular speed.
In a lot of ways these are silly examples, and there aren't too many good reasons why you should risk a high-speed abort after V1 - but there
are reasons where it could be a good idea.
TL;DR - Don't abort after V1 unless there's a damn good reason to do it, but sometimes it's better to be a test pilot and risk an overrun than take a sick airplane flying, or "think before you go fly."