I would strongly contest that there is a big 4 now. There is big 3 and Gretzky far ahead, McDavid could realistically make the trailing group 4 and he is the first player I have seen that I feel that way about unless maybe you count goalies(Hasek).
Only caveat is how Jagr look if there was no Lemieux or if he played today? McDavis is just a step above Crosby/Ovi for me but it's far from a given he eclipse them for career.
The logic behind the big 4 isn't necessarily to imply they are all 4 on the same level, but moreso that as a group they are a significant step above everyone.
For McDavid - or anyone, to join the big 5, for me it's less about him being worthy of being on same level as them, but it's more about him being a significant step above everyone else.
Also - although I do have Gretzky as a very easy #1, for height of peak, both Orr and Lemieux are right there with him. For prime/career, Howe mounts a heck of a case too. I do agree in my opinion he is untouchable at #1, but not enough for me to agree with a "big 1" following your logic.
Also, Jagr has pretty big weaknesses in his career. Unlike Crosby/Ovi/Mcdavid, he actually started his career a bit slow. Yes he won 2 cups early, but it's not until his ~5th season he started being in running for best in the world, compared to much earlier (2nd or 3rd season) for other 3.
Another weakness for Jagr is he lacks a lot on longevity of elite seasons vs Ovechkin/Crosby. Yes he played until mid-40s as a good NHL player which is amazing, but if you were to count elite, or even "very good" season depending on how you define the term, he lacks. He left for KHL, slowed down a bit in Washington, etc. Both Crosby and Ovechkin probably have a better 7th, 8th, 10th, 12th best season than Jagr. For McDavid it's too soon on the longevity part, but he's pacing Crosby very well age for age so far, so good chance he ends up passing Jagr too unless he somehow falls off a cliff.
Finally - Jagr was a very good playoff performer overall, but he lacks a true signature playoff run (let alone, multiple runs). That's another glaring weakness in his resume.
I say this as someone whose very high on Jagr's peak/prime, I think I may have him as high as #5 after the big 4 for peak. But with or without Lemieux, I don't think any of the above 3 negatives against him really change. I think he's one of the players who has an argument for #5 all-time, but definitely not the strongest of arguments.