Double after split?

So I’m used to playing slots but lately I’ve gotten into some blackjack at the live dealer tables online. My question is about splitting pairs and the option to double after that. I’ve seen some places let you double after you split but others just won’t allow it at all. When I split a pair and end up with something like an 11, it feels like a great time to double down, but then the site just won’t let me.

I always assumed splitting and doubling should be separate options but when you put your money in, you want to maximize every hand, right? For folks who have played a lot more blackjack than me, does doubling after splitting really give you much better value over time, or is it just a way for the house to look like they're giving you more freedom while the edge barely moves? Just want to hear some real opinions before I risk any more credits on these tables.