I believe that weak early type of weaknesses should be eliminated and replaced with an other weakness, because sooner or later they get out of control. what do you think¿?

We do not think of "this champion is weak early game" as a sufficient weakness, at least not to my knowledge. If I heard a designer justify a decision by saying this ("but my champion is weak early!"), I'd like to have a long and enlightening discussion with said designer where they can explain to me how that is healthy for the game.
(Spoiler: It isn't)
I think it's good for champions to have appreciably different power curves, don't get me wrong! I think it's great that different champions "come online" or "peak" at certain points in the game. It shapes the narrative of a game--oh man, if we don't get an advantage before Kog'Maw hits five items, it'll be tough to win the game--but again, it is not a SUFFICIENT weakness.
Let's talk about weaknesses for a second!
A weakness in a champion's kit is a hook to create gameplay for the enemy. If a champion was an all-rounder, equally good or bad at everything, and you played against them with a similar champion, you'd end up running at each other and stat-checking each other, and that would be that. In Starcraft Brood War terms (that's a contemporary reference point, right? I haven't aged horribly, have I?), it would be 1a2a3a all the time.
Xerath's weakness is that he is extremely helpless at close range. A number of factors conspire to make this true: his W has a fixed delay, making it no stronger at close range, his R has a fixed travel time, making it easier to dodge point blank (you get SO much warning), he constantly slows and roots himself making it easy for melee champions to wreck his face, and finally and most importantly, E's stun scales with the distance the missile traveled; this means that if you're on top of his body, he can only stun you for a very short time.
This creates gameplay! Your question now becomes, how do I get close to Xerath? Do I flank him? Do I build tons of MS or have my allies speed boost me? Do I wait for him to be shooting his ult and assume he's not looking at himself? Critically, this is universal gameplay; "kill this guy early game before he ascends to god-hood" is NOT universal gameplay. You miss that window, you're fucked for the rest of the game. I don't think that's good gameplay.
TLDR: strong early or strong late are good secondary qualities for champs to have but not sufficient weaknesses and aren't treated as such when weighing strengths vs weaknesses.