Why do small aircraft rentals charge per flight hour?
In the US most General Aviation rentals are "Wet Hobbs Time" -- You are billed based on the actual clock time the engine was running (in tenths of an hour), and fuel/oil are included in the rental price.

This is attractive to renters because of the simplicity: You don't have to pay the FBO separately for the fuel, oil, and aircraft, and you're basically paying for the amount of "clock time" you spent in the plane.
It's easy to understand, especially for new students who may not quite grasp the concept of how the recording tachometer measures "time".

Hobbs billing is attractive to the FBO as well, for different reasons:


Rentals are typically blocked out by clock hours ("10 AM to 2 PM").
Since booking is clock time billing based on clock time (Hobbs hours) makes sense.  
In practice the two numbers are usually close (and when they're not the error tends to favor the FBO).




Let's look at your "Tach vs. Hobbs" scenarios (for the sake of simplicity let's assume both flights are three "clock hours" chock-to-chock):

Pattern Work

Pattern work consists of three basic phases: 


Takeoff (full throttle, high RPM - Tach runs faster than Hobbs)
Circuit (low power, low RPM - Tach runs slower than Hobbs)
Descent &amp; Landing (near idle power, very low RPM - Tach runs MUCH slower than Hobbs)
There might be a taxi in there for full-stop practice, but you'll be close to idle there too.


If we average this out over three hours of pattern work (and assuming you and your instructor don't commit suicide to break the monotony) the Tach hour meter will be reading a number much lower than the Hobbs meter.
In this scenario you might have 2.25 tach hours for your 3 Hobbs / Clock hours.

3-hour Cross Country

A cross country consists of 5 phases:


Takeoff/Climb (full throttle, high RPM - Tach runs faster than Hobbs)
Cruise (moderate throttle, moderate RPM - Tach and Hobbs run about the same speed)
Descent (moderate-low throttle, moderate-low RPM - Tach may be a bit slower than Hobbs)
Circuit/Approach (low power, low RPM - Tach runs slower than Hobbs)
Landing (near idle power, very low RPM - Tach runs MUCH slower than Hobbs)


If we assume Phases 1 and 3 take about the same time they roughly cancel each other out. Phase 2 (Cruise) is a wash too, so we're left with two brief periods where the tach is running noticeably slower than the Hobbs (the pattern and landing at the destination).
In this scenario you might have 2.85 Tach Hours for your 3 Hobbs / Clock hours.


  In both of these scenarios the FBO comes out ahead of the game -- they're billing you for 3 hours of time, but their maintenance cycle is based on the tach. This might be enough to squeeze another day or two of profitable flying out of an airframe before it's next annual or 100-hour inspection.




There are scenarios where you can "beat" the Tach clock, but most of them involve being downright abusive to the aircraft/engine. For example if you flew that 3 hour cross country at low altitude and full throttle (very high RPM) you might rack up 3.3 tach hours for your 3 Hobbs hours. The FBO is basically stuck eating that maintenance expense.
Along similar lines when renter pilots abuse an engine (for example by leaving the mixture knob full rich for the whole flight) the tach time doesn't always tell the whole maintenance story - the mechanic's time cleaning the plugs because the next renter couldn't get through a runup has to be paid for somehow.