Bill Zebub
“It’s probably Matt Mercer’s fault.”
One thing to recognize is that spellcasting checks replace spell attacks and saving throws. Most of the time, when you succeed on a spell's check, it just does the thing. There's no saving throw on the monster's end (most of the time). So if you got rid of spellcasting checks, all spells would auto-succeed all the time.
Sometimes I think that people who hate the spellcasting check have not thought through this.
I think your method of giving one free cast is tremendously generous. With a casting stat of 14 and no other bonuses, and no spells beyond the default number, Shadowdark casters get more spells/day than in, say, D&D.