You have the yaw/roll switched. The TC's canted gyro adds roll to the yaw rate sensing, not the other way around.
The biggest drawback to the turn coordinator was the presentation of the aircraft, which to someone new to its use can tend to get mentally processed as a horizon bar, especially an old timer trained on aircraft with war surplus black face artificial horizons (with were widely installed on light aircraft into the 60s until surplus stocks ran out). The TC's little airplane tilting left could initially be mentally interpreted as a bank to the right in other words, until your conscious brain finished processing the information (Russian artificial horizons had this presentation where the gyro tilted an airplane symbol; transitioning to western style horizons can be a problem for Russian pilots).
A turn and bank with the vertical needle is easier to interpret at a glance. The problem with the turn and bank was since only yaw rate information was presented, and there is no internal damping, in bumpy air you ended up with too much "noise" in the information presented from the nose wagging back and forth. In an airplanes like V tail Beech Bonanza, which were quite bad for tail wagging in turbulence, a regular turn and bank could be nearly useless in the bumps with the needle slewing back and forth constantly in level flight. TCs avoid this by not just splitting the motion sensing between roll and yaw, but also by using internal dampers (little shock absorbers) to present only movement that is established.
One problem with TCs is that once you are stabilized in a turn, there is no more roll rate to sense, only turn rate and that has to be taken into account in the way the rate markings are placed.
My old '68 Cardinal had a TC that had gone bad because the internal damper had gone south. The thing jumped around like crazy because of the un-damped sensitivity to both roll and yaw. I replaced it with an older 12v electric turn and bank (way cheaper - Turn Coordinators are quite expensive because they are electric with internal inverters to convert 12vdc to 110v/400 Hz fixed frequency ac for the gyro) and found I had a strong preference for the vertical needle presentation.
Personally, I think the turn coordinator should have stuck with the vertical turn needle presentation, but with the damped canted gyro internals. Like I said, much easier to interpret at a glance.