I think you're missing something here. Spells almost always start and resolve in the same combat round (thus on each "turn" a caster could start a new spell). But in 5e terms how it'd work would be something like this: if your initiative is 15 that's when you start casting. Your spell has a listed casting time (say, 6) which means you won't resolve your spell until initiative count 9 and during the intervening time you're both open to interruption and have no active defenses as all your concentration is going into casting your spell.I can see the appeal on a tactical level, but I feel like as an individual player the gameplay loop wouldn't appeal to as many people. A lot of people don't like spending turns doing nothing: "You're up Elwyn, what do you do with your turn?" "I continue to cast my spell." "Okay, Gerald, your turn." It feels pretty passive,
Each spell has its own casting time, generally (but not always) increasing with spell level.I know I wouldn't really enjoy it. It also gives the caster a very heightened sense of importance, they become precious artillery that must be protected at all cost which in turn will make a certain specific play style more optimal than other almost all the time. If nothing else, you'd need the flexibility to faster and slower spell to avoid that.
Here I disagree. If you want to get into melee, play a melee character. If you want to get into melee as a caster, you're using such physical weapons as you have because you ain't casting. (unless your specific intent is to get interrupted and hope for some sort of interesting/fun/beneficial wild magic surge; I've seen this done once or twice) And if melee comes to you something's gone wrong somewhere...Casting in melee also has its own narrative appeal that's different from the frail artillery at the back and the game should have ways to do it.
As a pleasant side effect, this also does away with most in-combat healing. Healing IMO is something done between battles, not during them.