Yes, this is the 4e treadmill. You always have the same 55 to 65% chance as long as you boost all the right abilities and constantly upgrade your items etc.
You do not have that in 5e.
No. Instead there are very few bonuses available (stats capped at 20, proficiency bonus grows from +2 to +6 over the course of 19 levels gained, magic items are optional).
A fairly steady range of success rates based on growing numbers, and a fairly steady range of success rates based on no growth in numbers, are functionally the same thing.
If 5E a character can EASILY be way outside of the target range and the game is built to create these situations.
I don't think a character in 5e can EASILY be way outside the target range at all. What sorts of examples do you have in mind?
At higher levels the gaps will grow, but this is equally true in 4e.
In 4e, the difference between trained and untrained is +5 for skills, +2 for non-AC defences (before feats), plus stat spread which can be beween -1 and +6 or 7 up to 20th level, and +0 and +9 or 10 at epic. Glomming all those together gives typical spreads in the neighbourhood of 10 before feats and items (the latter typically are more relevant to skills than to NADs).
For my 28th level party, the biggest spread in NADs is 10, for Fort (invoker/wizard 32, sorcerer and paladin 41) and Reflex (paladin 35, ranger/cleric 44) - for Will the spread is 9 (fighter/cleric 39, sorcerer 47). For skills, the biggest spread is in Arcana and History (invoker wizard +42 to both, next highest being the sorcerer at +20 Arcana and +15 History), then Endurance (fighter/cleric +34, next highest +18 range/cleric). The only skills in which the spread between best and worst is not at least 10 are Heal (+23 vs +16) and Streetwise (+23 vs +15).
In 5e, the difference between trained and untrained (ignoring the expertise class feature) is +2 to +6 for skills and saves, plus the result of stat spread which can be between -1 and +5. At 20th level we can expect plenty of wizards with -1 to climb walls, and fighters with +11. That's a spread of 13.
DCs in 5e range from Very Easy (5) to Nearly Impossible (30). Easy is set at 10. The spread between Easy and Hard in 4e is 8 vs 19 at 1st level (comparable to 5e's Easy vs Hard) and is 24 vs 42 at 30th level (a comparable spread to 5e's Easy vs Nearly Impossible).
The level, in 4e, at which the gap between Easy and Hard roughly corresponds to 5e's Easy vs Very Hard is around the beginning of paragon tier: at 11th, Easy vs Hard in 4e is 13 vs 27.
So 5e played in such a fashion as low level characters encounter few or no DCs above Hard, middish-to-low-upper PCs encounter few or no DCs above Very Hard, and Nearly Impossible tasks are confined to upper level PCs, will have DC spreads pretty comparable to 4e.
The fiction might be different, but the mechanics won't be.
Also, any comments on the spread of DCs in the published adventures would be welcome!