Out of the game's 73 melee champions, only 3 do not have mobility in their kits

Those champions are Cho'Gath, Nasus and Taric. Effectively, less than 5% of all melee champions are currently designed to not rely on any mobility from their own abilities, and the last one was released over 7 years ago. By contrast, out of the game's 60 ranged champions, 17 have no mobility-enhancing effects, which is a little over 28% of the ranged roster (this number is also significantly deflated by the number of ranged supports, whose ally utility often includes bonus movement speed).

What this basically means is that, anytime Riot wants to design a new melee champion, you can bet that they'll have some kind of in-kit mobility somewhere: most of these melee champions tend to have some kind of persistent, relatively minor amount of bonus movement speed (Mordekaiser gives himself 75 bonus movement speed for 4 - 5.5 seconds, for example), but most recent melee champions have had dashes or blinks instead, and sometimes a combination of the two, as is the case for Camille. In practice, this leads to a lot of repetition: mobility creep has been talked about for quite some time, and it's difficult to deny when every new melee champion is expected to have some kind of gapcloser, or at least enhanced movement of some form. Because every new melee kit is liable to have at least one slot taken up by a mobility ability, that also tends to constrain design decisions a bit, and there are only so many variations of a dash that one can have in the same game.

Beyond that, though, what this suggests is that the base movement of melee champions is insufficient: if melee champions were able to navigate fights just by moving normally, they wouldn't need nearly as many movement speed boost or dashes as they do now. Even juggernauts, who are supposed to be among the least mobile champions in the game, and who therefore should not have mobility as a big part of their power budget, practically all need enhanced movement to be able to function, and even then, they suffer horribly against teams that can kite them adequately.

The problem becomes clear when you look at base movement speed across champions: although ranged base movement speed is (usually) capped at 340, and melee base movement speed at 355, 35 melee champions (about 48%) have base movement speed equal or inferior to that of a ranged champion. Only 13 melee champions exceed 340 base movement speed, and yet one of the champions with the highest movement speed in the game is mini Gnar, a ranged champion (though he's a bit of a special case, along with Cassiopeia, who has 400 movespeed at level 18). What this means is that, in order to reach a ranged champion, the average melee champion has to approach them with significantly less attack range, but also little to no additional movement speed, sometimes even less movement speed than their target. Without a gapcloser or some other kind of drastic leverage, the melee champion stands no chance, yet that leverage is also threatened in an environment where a large amount of ranged champions, a significant majority even, have mobility of their own.

TL;DR: Melee champions are currently being designed around too little base movement speed, which forces their kits to almost always include some kind of mobility, which itself limits the breadth of what can be done with a melee champion, and often creates other balancing issues that have affected the game for a long time (e.g. inflated stats on melee champions, which has led to noodle fights in top lane and tends to make combat against ranged opponents more binary). Melee champions need a roster-wide increase to their base movement speed, which should allow many of their kits to have their mobility trimmed down or even stripped completely, and thereby give future melee champions a chance to thrive without needing some kind of innate gapcloser or movement speed boost. No melee champion should be slower than a ranged champion, even if they're a juggernaut, or some equally slow champion like Blitzcrank or Nautilus.