During my early training, I too was apprehensive about spinning & I was definitely uneasy as in those days it was a mandatory requirement. Shortly after starting my PPL course, the rules changed and I was somewhat relieved at not having to do the exercise.
However the bogeyman wouldn't go away and very soon after I got my licence I grabbed an instructor & headed off for a lesson in spin training and recovery. I briefed myself thoroughly beforehand and mentally rehearsed the recovery procedure until I'd convinced myself I'd be able to get it right first time.
I made sure the tomahawk I'd booked out was one of the ones with full harnesses & spent about 10 minutes extra on the walkround removing all the pens, paper & other rubbish from the cockpit. Waiting for the instructor, I rehearsed exactly what I'd do with the controls once the spin started. I felt very confident I'd be able to recover from a spin without help from the other seat.
We climbed up to about 5000ft in the training area and after a couple of clearing turns I realised this was the moment to put it all into practice. Chopping the power, I pulled up into the stall and just as the aircraft stopped flying, gave it a bootful of rudder.
I simply couldn't believe how quickly it entered the spin & in spite of all that preparation, instinctively tried picking up the dropping wing with aileron. The windscreen was suddenly full of rapidly rotating fields & I was pressed hard against the side of the cockpit. A few turns later my instructor took control & recovered the aircraft as I felt my overconfidence rapidly being put in its place by a generous helping of reality.
After climbing back up for a second go, I was better prepared for how the aircraft would react & managed some semblence of controlled recovery, though it didn't seem to be climbing as well as it usually did. It did, however, climb much better once my instructor told me to remove the full opposite rudder!
After another hour of spinning it in both directions, I'd got to the point where I could keep the height loss to 1500ft & felt comfortable with being able to do it for real if I somehow managed to spin it by mistake at altitude.
I've never inadvertently spun anything, but I have had the occasional close encounter and I do believe real experience of spin recovery is an essential part of pilot training. It demonstrates that the onset of loss of control can be violent and disorienting, but prompt and correct recovery action will put the cows back in their proper place. There needs to be some element of muscle memory in this; you're likely not going to be able to work it out calmly and rationally in the heat of the moment.
As Pace said, there's been a spate of fatal accidents involving loss of control at altitude, and it's at least possible that the lack of spin training in the current syllabus might have been a factor.