Yes, the downside of long-duration spells is the tracking. I think simplified durations are the way to go.
Apart from the usual "until the end of (somebody's) next turn", "sustain (action type)" and "save ends" durations, 4e also had "until the end of the encounter" and "until the end of your next extended rest" for longer-duration effects.
"Until the end of your next extended rest", is (IMO) a pretty good duration for really long-term effects that can be swapped out on a daily basis (unlike feats and class features). "Until the end of the encounter" probably needs to be reworded to remove the encounter stigma, but tying the effect duration to the standard duration of a "short" rest (or the 5e equivalent) and then making explicit the potential balance issues in de-linking the two durations might work. There could even be some flexibility in tying the spell duration to the duration of two, three or more short rests - the onus would be on the PCs to fit as many combats as possible within the time frame to maximize their advantage, of course.
The return of the concentration duration might also be interesting, with the proviso that a spellcaster can only maintain one sustain (action) or concentration duration effect at a time. The difference could be that whenever the spellcaster takes damage, he must succeed at some check or lose the concentration duration effect. Actually, given the way that actions seem to be playing out in 5e (everyone gets just one action per round, plus free actions), sustain (action) might no longer be applicable (expect for major effects that you are willing to give up your one action per round for) and concentration might be the way to go.
Since it seems likely that caster level will no longer affect spell power, we will probably also not have (round/minute/hour) per caster level durations. That said, it should be possible to extend an effect's duration by preparing it in a higher level spell slot. Perhaps as a 1st-level spell, it lasts for the duration of a short rest. As a 3rd-level spell, it might last for two short rests. As a 5th-level spell, it might last for four short rests, and as a 7th-level spell, it might last until the end of your next extended rest.