The first question the OP implied, do I think the addition of more lower level spellslots will compensate for the loss of the higher level ones? That answer to that is no. In my experience (I have run one campaign that ended at 20th level in 5e), casters have enough of the lower level magics, especially when rituals are factored in, and those magics are not the equal of the higher level powers. So this houserule is a nerf to high level casters. Whether your group believes casters need a nerf at high level is completely up to your group, but I would say this is one.
What do you think of the idea of the extra slots translating into a spell slot "pool" they could draw on for any spell of level 1-5? At 20th level this would be a pool of 28 spell levels, which could be quite a few extra mid-level spells.
Also, do you see my point about how powerful these high magic spells are? They can easily shift the course of an encounter, and while I think being able to do them once or twice is fine, having 4-6 of them is just too much. It means for most random encounter "adventuring days" they can use them very freely. I mean, we change things up so what starts as a random encounter turns into a full blown adventure with several encounter before a long rest, but as a DM I don't like to resort to this too often.
Then the question comes down to...is the problem your trying to solve preventing the "nova" or the "everyday nova". For example, one houserule I've been tinkering with is the notion that high level magic slots are per adventure instead of per day. But they would keep their slots as is...or maybe even have more slots. So this means that a caster could throw down on a given day when they need to....but once that high magic is blown, its blown for a long time. Part of my desire for this is just to change the world issue of "why don't high level casters just run everything". If high level magics are literally moments of story, powers that a wizard may not recover for years (at least for npcs that don't adventure)....then it makes them a lot "cooler" and less spammable.
A single encounter NOVA I am fine with, which for many encounters I consider a single high magic spell. What I don't like is multiple novas between rests.
I think restricting them to per adventure might be too harsh, but I know you mentioned giving them more slots, so it might balance out. However, then nothing would stop them from using 2 or more high magic spells in an encounter!
From this idea and some of the earlier posts, I am sort of leaning towards the idea that you can only recover one high magic slot per long rest. So, after resting in town for several days, you are full up. But, once you use a slot, you will only get that one back. Use another, and suddenly you are down one likely until the current adventure is over. Use another, and now you are down
two, etc.
For me, this represents the idea that the caster with ample time to prepare is as ready as possible, but once danger is lurking it becomes harder and harder to replenish those powerful spells. What do you think of that idea? I might be able to go with that one...
' Part of my desire for this is just to change the world issue of "why don't high level casters just run everything" '
Yeah, they would IMO.
I know in our final endgame for our main campaign we are facing a CR 23 Wizard while multiple high magic. As a DM, I don't see us winning this fight... I know a wizard, especially since we have to face him on his home turf, is going to be nearly impossible to defeat. I haven't seen his info, but I know our DM and our first encounter with him he was so cocky he used a
wish spell to return on of our dead comrades to life, just for the fun of it.