The downside I see is the same as you get when buying a tv/dvd or vhs/dvd combi unit. If one side of it stops working you have to buy a whole new unit if it can't be repaired - big £££. If you have separates you only have to buy the one item - a lot cheaper.
Most/all tig inverters will stick weld but I think I would still like a separate mig welder. Even though I have an inverter I still use my oil cooled for stick welding when I can - always a fear of my inverter going bang & leaving me no tig welder!
The multi process machines are good and have there uses. I have the oerlikon 200 mp .
I mig with it. Then swap to stick depending on the job. But as said....if one of the processes goes down then so does the whole unit. My machine stopped working in the middle of a job. Completely dead..had it sent off . The main board had fried a circuit thus making making the unit scrap. It was replaced under warranty. I still have the machine but don't really use it now. I will be going separate units.