Tom,
The primary reason for the pack layout of modern aircraft, with heatexchangers, acm´s and so on, is to remove as much heat AND water as possible.
As you correctly state, it is possible to use heatexchanger cooling only, and if you could keep a sufficient cooling flow over the heatexchangers this would be a good cheap alternative, the problem is the amount of cooling air needed, you would only get this amound with a relative high speed, probably 150 kts or you could inrease the size or amount heatexchangers.
An ACM is used primarily because for a low weight you can remove alot of heat from the air, so much that you need to reheat it to stop ice from forming. To answer you question about wether or not the bleed air pressur is sufficient to drive the cooling turbine, No it is not. For the turbine to become effective you need to have it loaded, hence the connection to the compressor and cooling fan, and it needs an inlet pressure around 200 to 250 psi to give a propper expansion and thereby cooling.
Regarding your question about Tip clearance in jet engines, there are systems to activily measure the tip clearence, the use eddy current. But due to their size they have no aviation application. Most modern jet engines GE90, PW4000, V2500, CFM56-5/7 and RR RB211/Trent have a "Heat expantion" schedule programmed into their Engine controller and the cooling is then based upon this schedule biased by RPM and Altitude. Older engines like PW JT9D-59A/70 or CFM56-3C used a trigger signal (RPM, Slats, Airborne and so on) to start a Timer that would give cooling air for a certain time, it wasn´t as accurate as todays but it was better than nothing.
Hope this wasn´t too long an answer.
Brgds
Doc