Separates you have to deal with the extra space requirements which is a big hurdle for most home kitchens, the extra cost of power/fuel, doubling up on venting and combining ducting or going with a custom single construction for the vent
With the sort of venting you're likely to need there's an extra range of hassles. You'll be putting a lot CFM out of the house that has to be replaced. If it's done incorrectly, you can poison yourself with carbon monoxide from your furnace. You're also venting conditioned air you paid to heat/cool, so you'll probably benefit from a heat exchange system to pre-heat/cool the replacement air with what you're venting.
If you're in a condo or HOA situation, there could be other restrictions.
As to induction vs gas: Gas stoves are about 33% efficient. So your hard to find 20K BTU burner is only putting 6600 BTUs into the pot. Induction is about 85% efficient. An easily found 3300 Watt burner on an induction cooktop is about 9500 BTUs into the pot. You get a lot more heat into the pot with the same instant response as gas with induction and a much simpler surface to clean. Simmer is easliy set on induction, even the most powerful burner without regard to pot or content size. Few gas burners do simmer well with all sizes of pots and volumes of water. An induction cooktop costs a lot more though.
It's worth talking to a number of different professional kitchen remodel people. Have them come out and give a bid, and check some of their design ideas for your space. It can be quite apparent who really knows what they're doing. I had about 4 or 5 different ones come out. Only one checked joists, power, water and gas lines and where they ran. The rest all said, sure we can do whatever you want, but it was clear to me that only one really understood the issues. And even still, I ended up with three extra beams and supports to do it right structurally. There's always some surprises once you start disassembling a structure. He cost more than the others, but his expertise was worth it.