"Cheap" is a non-issue here when Mobis and Swifties are the exact same price.
For that same price, you can get either 65 constant MS, or 105 MS that instantly drops down to T1 boots level the moment you hit someone or get hit by something.
To that end, Soraka is probably the ONLY champion who makes noteworthy use of Mobis since healing allies doesn't disable the speed boost, but even then landing a Q or E will deactivate them. And possibly Janna, but again, doing anything besides using your shield deactivates them. You don't want them on anyone who can poke because you LOSE MS for poking with them. And Bard, for roaming around collecting chimes and doing Bard things.
As for trying to engage with Mobis, that's all fine and good if you have the element of surprise. Otherwise they can just throw something in your general direction and instantly knock 80 MS off of your engage. (Or you're Blitz and your ult passive randomly shocks something and disables the boost, but that's more an issue with Blitz's ult than the boots.)
The tradeoffs would be fine if Mobis were actually cheaper than other options, but at that point they crowd out other options, as was said before. As it stands, they aren't, and I can't see any real reason to ever use them over the consistently reliable Swifties.
If they really wanted to keep the Mobility effect, just fuse it with the Alacrity enchantment.
"Alacrity: Grants +20 additional flat Movement Speed, increasing to +60 additional flat Movement Speed when out-of-combat for 5 seconds."