I'm 5'7" and I just measured my lower leg to see if it was 18". It is just under 18". If I were to step over the 18" tub I'd have to get on my tippy toes. If you never take, but the occasional bath, I'd go with the Villager as Writersblock suggests. If you don't like the Villager style, the standard alcove replacement Bellwether has a nice modern look yet is only 14" high like the Villager. Easy to step over, and it can still provide a bath:)

Do you have a specific tub in mind? We have a Bain ultra air tub and I couldn't imagine showering in it every day. The acrylic bottom along with the added height of the side.... to me it seems like an accident waiting to happen. I guess it would depend on the height of the tub you had in mind. In regards to the automatic air purge, it only happens after the air cycles off. You wouldn't be turning the motor on when you shower so the automatic thing wouldn't happen.

You can get a 5' "soaker" tub with wider stance and deeper seat for about $200. For a 5' jacuzzi (check out the one fifth on the list), it'll run you about $800. Both take only a couple of inches either direction than a "standard size" tub.

That alcove is designed to house a tub only, not a tub shower unit. You can't "repurpose" what's there without water damage to your floor, window, and behind your walls. The tub itself not designed to be used that way, and neither is the window designed to be in a wet area. You'd need to rip it all out and start over by installing a smaller and waterproof window, then installing a tub that had an integral tile flange which is part of the waterproofing system needed. Then your waterproofing membrane and whatever wall cladding you might want.