Nudging Steel - yes that is quite often the case at busier airports - once you know you won't need to do a go-around due to traffic on the rwy etc.
The OP seemed more to be asking about cruise flight I thought and yes you probably would notice as at altitude big jets are a bit finicky. I am only familiar with 737s up to -800 series and if the autopilot is unservicable we are not actually allowed to fly higher than 24,000 feet or longer than a 3 hour stretch. Plus I think you may only operate to a repair station. (don't have a MEL/DDP handy so off the top of my head).
Normal levels for us are 37,000 to 41,000 and we can do up to 5 and a half to 6 hr stretches. So it would be quite limiting - not to mention the extra fuel used at low altitudes.
But as other posters have said flying up to or from 10,000 feet is reasonably common - to keep skills honed - but again preferably not in busy airspace as the non flying pilot then has more work to do if you are concentrating on manual skills.