Are the Valentine Event Gotcha CEs necessary?

Gacha CEs are never necessary to clear an event.

That said, finding a Waver/Merlin/Jalter/etc. with a gacha CE on your support list won't be difficult and you should totally be picky about borrowing the best one.

I didn't do any calculation. But think in this way: how many quartz you need to roll these CEs? And how many AP's you can get by consuming these Quartz? While the 5* CE is decent, there are many better options there.

My experience for most events is that you can clear them (without monuments/pieces) with natural APs. And occasionally, you need to consume a few apples..

I would really not spend rare prisms for Melty Sweetheart just for their bonus. Once you've save enough to buy the new Shop CEs, they'll provide the same bonus. What I found from last year is that once you get the ball rolling with shop CEs, you'll end up with more CEs than you can use.