She wasn't mentioned in TBBT just because her character was created around the time tbbt was ending. But sure, to make it logical (in line with tbbt), they could have made it so that Paige was his love, but it ended very tragically.Along with that and the death of his father, Sheldon became withdrawn, broken, and more anti-social and against relationships...
There were also hints in YS that there might be something between them. They always had a special relationship that included a lot of emotions. They were rivals, friends and more. They teased each other, had fun, were jealous sometimes, etc. Sheldon always treated her differently than the others (he also did things for her that he wouldn't do for anyone else). They also had a concern for each other and I think definitely a soft spot, although it was never confirmed (especially episodes 5x17 and 6x13). Paige was a challenge and an impulse for him (emotional, intellectual), they competed, but also helped each other, there were several emotional moments and the development of Sheldon's empathy.
Paige is a great character (my favorite), very likeable and interesting, but also wasted. Great potential, great possibilities, but it's all limited by TBBT, where it was said that Sheldon doesn't show interest in anyone and that he's never kissed anyone (plus, it already has a designated direction and a written end: so we know that X things simply cannot happen)... Paige never had a chance to have a more important role and be a (better) friend to Sheldon, let alone his girlfriend.
YS and TBBT are two completely different shows anyway and completely inconsistent. It would be better if YS was a stand-alone show that didn't have any limitations (new characters, new storylines, limitless possibilities). If it wasn't a prequel, Paige and Sheldon would definitely end up together (great chemistry, complex relationship, good compatibility... Sheldon had no chemistry with Amy, no romance, no spark...). YS could continue, Sheldon could develop better and earlier, George wouldn't have to die (at least not so soon), Sheldon wouldn't have to go to CalTech, etc.
Damn prequel problems.
