If you're asking for honest opinions, OP, I wouldn't do that. My almost 14 month old used to only contact nap, now he'll do pram naps as well thank goodness but I do get it's hard graft. But I used to consider the contact naps my downtime. Can't you watch Netflix on your phone, volume turned right down or with headphones? Tbh when mine was only contact napping, I only watched TV with DH after he'd gone to bed - bit extreme but I'd literally forgotten Netflix on a mobile existed 😂
Mine also has a massive playpen, maybe we have the same one. He only goes in it when I'm prepping his food, trying to cook or clean something like his highchair post-meal or the floor (I get him in and out when he's not happy or for a break). I don't think he's ever done a 30 min stretch, he was in it for more time over the day on Christmas eve and the day before his birthday while we were prepping food but he had me, DH and his uncle in the house entertaining him whenever needed. He does play in it independently and I do think that's important.
I just don't get why you need a 30-60 min break from your child first thing though. It's obv become part of your routine but that's quite a while not to be interacting with them at all, and just for watching TV. Can't you have your coffee while they play next to you? Maybe they're a bit burned out of the playpen by the time it comes to you prepping dinner, you mentioned in one of your replies quite a few other times in the day that they're in it. I would also look at outings you've chosen as quality time / a brain break no?
Screen time - I do think it's really unnecessary for a 10 month old and if you treated it like it wasn't an option, there would be a viable alternative while you make dinner. A PP suggesting playpen with the monitor on is a good one.
I found making batches of freezer food re really helpful with mine, like a batch of pasta sauce and half filling a XL silicone ice cube tray, it really cut down the time spent making dinner cos you can just prep pasta/rice/steam some veg etc