I get the argument for using new balls in nets, but I wouldn't say that using an old match ball means there's no swing or movement. If anything, depending on how well you've looked after your old spares, there's sometimes more. It also adds more challenge to the bowler to look after the ball and practice bowling later in the innings. Not sure about everyone else, but I rarely bowl my opening bowlers all the way through, I often keep them back for later on, meaning they need to practice with an older ball as well. And for batting, being able to face an older ball that's a bit softer is useful, it won't ping off the bat immediately and requires some effort and a different technique.
Up until this year, as Captain I carry an inordinate amount of spare match balls around with me. I'm happy for actual bowlers to use them for practice, but they keep them in good condition and because they do, it is actually a benefit for any matches I need the spares in future. I'm not a bowler, never have been and never will. So, can't speak from personal experience but the bowlers at my current club and previous clubs seem very happy to look after and practice with old match balls. Especially in winter nets when they're really just getting into a rhythm again, trying to bowl in the channel around off stump and want to use a ball that will be used in actual games. We have a range of old spare match balls of various ages and bowlers select from it accordingly (or bring their own they've managed to nab an old match ball last season - tut tut).
Once we go outside, we're more likely to use new balls during various drills with (or more commonly without a batsman there) so that the openers aren't completely surprised when they run in for the first game with the new ball. This is going to sound weird, and I don't always treat them like children just sometimes, but the excitement the openers have when they finally run in with a new ball and it comes out faster, bounces, nips off the seam and beats the bat. Seems to get them up for the game, since they haven't bowled with a new ball in a while and haven't been beating the bat of poorer batsman in nets at all.
New Captain this year though, and I'm not precious over the above process (despite how anal it sounds). So, have handed the spares over to him and will be following his lead.