If we are going by the guidelines without days off, we have 1 to 20 in a mont or so.
6 to 8 encounters per adventuring day.
About 12 encounters per level.
So that makes 2 levels per 3 days... Or 20 levels in 30 days...
As someone who likes campaigns where other things happen, where there are events going on and BBEG plots unfolding, the idea of a 20 levels in 30 days kind of thing, or there always being a world ending cataclysm to prevent, makes me sad. There needs to be more downtime, and things to do in downtime, in the game. Now, a DM can always add it in, but its all half baked in support of the "let's play the next major adventure book from level 1-15 over a couple of sessions and save the world (again)".
As have been mentioned, I'll second that Feats, Backgrounds, Classes and Subclasses can all cover for "holes" in a party. But there is plenty of healing without clerics, heck, just the "long rest recovers all HP" is all you really ever need, unless that entire adventure (and multiple level gains) all happen in one day? Ugh.
But, that "jack of all trades" ability is a design choice in 5e, and a feature for some, not a bug. Particularly when you can just grab whatever class, race, background, and feat (if being used), or heck, multiclass (if being used) to be able to do everything reasonably well. And with how CR works in the core rules (i.e. a joke), most new players and DMs won't find it particularly difficult to play whatever type of game with whatever someone wants to show up with (optimizing and sub-optimizing aside). Again, many find that a feature, not a bug.