If everyone's playing an MMO but they're all on their own server, it's only an MMO in namesake, not in gameplay or feel.
While it would certainly be misleading to say "Elite Dangerous is not a MMO", it's not exactly following the typical genre conventions of one either.
I've occasionally seen the term "Massively Single-Player Online" for games in that sort of niche - you can meet up with other people but it's not necessarily expected that you will; most inter-player interaction is indirect and asynchronous - but it's not exactly a widely-understood term that Frontier can advertise the game as.
That said, the main problem with meeting up with other players is not the modes but the map scale. The two systems I've spent most time in lately, looking at the traffic reports:
- one of them is just me, and maybe a player a day present in supercruise for a minute as they jump to somewhere else
- one of them has a bunch of haulers (traffic report pretty much purely T-9, T-8 and Cutter) probably doing 5 minute "supercruise to station, load, hyperspace out" trips. The total traffic report is about 40 ships, so the system is going to be occupied for maybe 3 hours out of the entire day. I sometimes see people there at the weekends, but it's not like there's much interaction possible beyond saying "hi" since we're both hauling different cargoes to different places on our own schedules
- there are some Powerplay systems nearby, which I've never seen anyone else in. Can't remember what the traffic reports look like - but they're right on the back of the Power's space facing the fringes of the bubble, so no other Power can plausibly attack them anyway. PP2 brings the "the map is huge" problem to Powerplay, so 99% of the time it makes no difference what mode anyone is in because no-one else (and certainly no-one else from another power) is going to be in the system anyway
- colonisation has just doubled the size of the bubble and spread people out even further
If Frontier had thought about this a bit more pre-release in 2013, and wanted to encourage same-instance interaction - which at least back then, they did - they'd have made the bubble considerably smaller (perhaps 1000 systems at most) and not kept the exact FE2/FFE setting. Obviously with colonisation they've decided that possibility is entirely messed up, and see no harm in it getting much bigger and player meetups being by appointment only.