I do take a seat for DS onboard. We didn't fly until he was 3.5y and I installed his seat FF even though he was RF in the car at home. We strap his seat to a folding luggage cart and wheel it on. It has to be carried over the seats on some planes (narrower aisles). Stow cart under plane seat, install carseat, install child. ;)
If traveling with DH and DS, I board before they do. I have multiple life threatening food allergies, so I have to wipe down all the surfaces, anyhow, and almost always get priority boarding. I take that chance to wipe everything down, install the seat, and stow my carry-on. Then I'm all ready when DS and DH board. If it's just me, I make do with DS staying corralled in one of our seats while I wipe things and install his seat.
We don't check the seat. I've seen seats be mistreated in the visible luggage areas (conveyors onto the plane, carts, etc) and who knows what goes on behind closed doors. I would not be comfortable using a checked seat. And rental seats have an unknown history. It's nice to have DS' seat with us in case of delays or travel changes, too. On a recent trip to Indiana via Detroit, our flight got cancelled. They were having a heck of a time rebooking for the next day and I offered to change my itinerary if the airline would do so free of charge--also keeping them from needing to put us up in a hotel overnight. Driving from Detroit wasn't hard for me as my eventual destination was between Indy and Detroit. I called DH and he handled my car rental changes while I dealt with the airline. Since I had DS' seat, I was good to go. Our checked luggage ended up in Indianapolis and was delivered the next day to our eventual destination (northern Indiana) after being flown back to Detroit and then to South Bend before being hand delivered to the town where I was staying.
I either strap my carry-on over the carseat while it's on the cart or DS rides in the seat while it's on the cart. It's easy enough.