All right. In light of these sweeping changes to available character classes, I don't think not being able to choose race or ability scores will matter.
I was slightly worried that being stuck with high mental abilities wouldn't be useful enough anymore, especially Charisma, since the addition of the Swashbuckler and Ninja lessen the blow on Int and Wis, but if you can't fix a high Cha with the switch you might be forced to play Paladin.
Maybe I missed it: What are your players thinking about your ideas?
I have not presented it yet. In fact I have not announced that I am working on a campaign at all, as I don't expect to launch it anytime soon. The intended players are mostly the same ones that I am currently playing with in another campaign. Once I get a good idea of what I want and what works best I will present it. I also wanted an objective perspective which is why I asked here first.
Since you want to emphasize martial characters and seem to be determined to use the D&D ruleset, maybe you should have a look at
Iron Heroes. It could save you a lot of work and make sure game balance is still pretty much unchanged besides the rarity of magic.
The idea behind Iron Heroes sounds like it could work for my campaign at first, but I might want to slowly increase the availability of magic in later stadia of the campaign, I'd have to see if I can find the books to see how different Iron Heroes is from D&D and to what extend material is interchangeable. For example, from what I read on the wiki-article, Iron Heroes does not have different races.
I made a few test rolls, and I think the biggest problem I see is not even the fact they're set to particular scores, but the differences possible. Even though this is just as likely to happen under the standard rules.
Take for example these two scores I rolled:
Str 18, Dex 12, Con 17, Int 14, Wis 12, Cha 10 (+11 mod/42 pts)
Str 10, Dex 11, Con 16, Int 10, Wis 7, Cha 10 (+1 mod/18 pts)
Unless one of the two switches some scores, the first character is better than the second in every ability.
In this set I also rolled:
Str 16, Dex 14, Con 9, Int 10, Wis 15, Cha 15 (+8 mod/35 pts)
Str 14, Dex 15, Con 6, Int 17, Wis 12, Cha 18 (+10 mod/42 pts)
That second character isn't gonna be really useful if these were the 4 members of the party, so I need to think of a way to lessen the differences between rolls, maybe roll a d6 for each ability and add 9 to the score, re-rolling anything you already have until you rolled all 6 possible results. Basically this gives a standard array of 10, 11, 12, 13, 14, 15 (+6 mod/28 pts) but randomized.
Trivia: However unlikely, it is possible for two players, both using standard ability score rolling rules, to come up with scores worth 12 pts (+0 total mod) and 84 pts (+24 total mod), 12 pts being even less than the default scores given to creatures in the MM, which have 15 pts.