Selling the emergency exit row seats
They do.  

If you are clearly not physically able, they will change your seat during check-in.  

Then, as part of the safety briefing, you will be explicitly asked if your are willing and able to carry out the relevant instructions.  If you are not, the crew has the authority to re-seat you.

If all passengers are seated, and no-one is in the exit row, the crew will re-seat a capable person next to the door.

Here's but one reference to the requirements from the UK CAA.