You need to understand that "radar service terminated" does not mean that IFR was cancelled. It simply means that control of your IFR flight has been transferred to the tower and they will be using non-radar procedures to keep you from running into any other IFR aircraft, and keep you at safe altitudes. See-and-avoid is the rule for you to miss VFR aircraft, just as it is when you are in VFR conditions with radar coverage. Remember that even when you are on an IFR flight plan, ATC is not required to give you traffic advisories with VFR aircraft. They will normally do their best to do so, but it is a "workload permitting" service, and I can guarantee (from watching TCAS displays) that in busy locations (entering/leaving Chicago Class B) they don't have time to call all the potential VFR targets for everyone.
When thinking about "radar service terminated", just realize that the conditions that you are entering does not allow ATC to talk to you and see you on radar at the same time. In the situation that you describe you are talking to the tower and they do not have radar, or if they do it is for their "situational awareness" only, and may not be approved for traffic avoidance (kind of like a pilot using a VFR handheld GPS on an IFR flight - helps, but not to be used primarily).
Similarly, "radar service lost" can (and does) happen in rural areas when you descend below radar coverage, such as below 3000-5000 feet on an approach in certain areas of northern Minnesota, Wisconsin, or the Upper Peninsula of Michigan, and is the equivalent to "radar service terminated". You can even lose radio communication and still be on an IFR flight plan, and ATC will not allow another IFR flight into the same airspace until you cancel IFR. In some places you have to call Flight Service on the telephone after landing to do so, and it may even require a land line instead of cellular (gasp!). In this situation you will not be talking to anyone, yet your airspace will be protected and you will be assigned altitudes and routing to keep you out of the dirt. Just like in the good old days when there was no radar coverage over the country, they use tools other than radar to keep aircraft separated. Even today, if radar in an area fails IFR aircraft can still fly through that area safely, since ATC will put them on airways and use timing to keep them apart rather than watching them on radar. ATC control of IFR flights is not necessarily synonymous with radar procedures, although most people tend to think of it that way.
