Re: Why does tower have to call to authorize practice approa
"Practice approach" implies you want vectors to the approach and a clearance onto it. Once you're cleared, you now require separation with other IFR aircraft, so this is something that could require coordinating with Regional Approach.
If you're just flying the profile without vectors or a clearance onto the approach, then it shouldn't matter. As long as you're staying out of the bravo, you could depart VFR and never talk to Approach, then just call the tower when you're back on final for the option. I'd recommend monitoring the tower to make sure you don't get in the way of anyone on final unintentionally.
Airports where ATC can say "no separation services provided" are determined by a local standard operating procedure and may change from time to time. At waco we have a primary airport and two satellite airports that we shall provide separation of VFR aircraft on a practice approach. For the remaining satellite airports we don't. This is outlined in our local procedure.
What you're experiencing could be a change in local procedure, selective application of that procedure by unwilling or unknowing controllers depending on who you get, or confusion raised by the fact that you're asking for a "practice approach" but just want to fly the profile yourself. I'd try avoiding the phrase "practice approach" and specifying that you want to depart VFR and just fly the profile with no vectors, or just wanting to depart VFR in <cardinal direction> and then just flying it without trying to explain it to ATC. I would expect you'll see more consistent handling with that kind of explanation. I expect right now you're getting controllers half the time that think you want one thing, and the other half thinking you want the other, so you're getting mixed experiences.
We get VFR aircraft on flight following all the time that say they're going out for maneuvers, and after observing them for a short time, it's pretty obvious they're flying on an approach (their track lines up with our radar map depicted approach paths). This is perfectly normal and legal as long as you don't bust any airspace and let approach know when you're back inbound and need to talk to the tower again. There's nothing wrong with doing this, and if you get in the way of other itinerant arrivals/departures, we'll let you know. But in Class E airpsace, there's really no separation minima for VFR aircraft, so you should be able to complete your practice without having to deviate too much.