Here is my most recent update/findings.
My SP/C character (who did not go to college) is now at 40 career pitching starts at the MLB level, and has unlocked all 23 hitting perks, 11 of the 14 pitching perks, 10 of 11 fielding perks, and 5 of 9 baserunning perks.
I still get offered the 'bugged' dynamic hitting challenge with a perk reward while batting (the one that is impossible to complete) - even though I've already got all the hitting perks.
I haven't unlocked a new pitching perk in over 10 starts, which is seems odd to me - they've all been complete game shutouts (or better - I did mention I'm playing on low difficulty).
For baserunning, I only recently started to improve those stats, and my habit had been to skip most baserunning opportunities, but I now have 37 carreer SB, which is probably why I've started unlocking those perks.
One other thing that concerns me... In one pitching start, I got the notification that I was injured, which I decided not to accept, so I hit the 'simulate and exit' choice (I had autosave turned off) to quit the game. In the post game progress screen, it indicated I had unlocked a pitching perk (Last Stand, I thnk), but since the injury result had me sidelined for 2-3 months, I decided to exit and reload my save. That was over 10 starts ago, and no additional pitching perks have unlocked.
I switched back to my SP-only character (who did go to college - so a headstart on unlocking pitching perks) for a comparison, and am now at 25 carreer starts in MLB, and has unlocked 12 of the 14 pitching perks, and 5 of the 11 fielding perks. My most recent pitching perk unlock happened in start 19, and I can't remember how long it's been since I unlocked a fielding perk.
I finally did experience a potential perk reward in-game challenge as an SP, but it was a Boss challenge, not a dynamic one. I once again found myself pitching into extra innings (zero run support from the offence), and in the 11th with the score still tied at zero the opponent's cleanup hitter came up, and I got the Boss challenge. Only one of the 3 potential rewards indicated a perk, but it looked the same as the 'bugged' hitting challenge - color indicated an unnamed hitting perk, and even though I seemed to achieve the task (strike batter out on 3 pitches), the challenge did not complete, and only 'failed' when I got removed for a relief pitcher after the 13th inning. It seems that one is 'bugged', too.
I also find it odd that the only way for a SP-only character to improve one's Speed attribute (which would still be needed to cover 1st base on ground balls) is through off-day training sessions - which means 1 point at a time. There's no way to spend tokens to do that.
I see that patch 8 has been released this morning, and the patch notes once again don't mention anything about fixing perk-related problems in RTTS.
I guess more testing is needed.