As a compromise position, since I myself have definitely desired mastery properties and fighting styles on my blade warlock:
1. As noted above, boost the final Warlock invocation by incorporating Fighting Style and Weapon Mastery. They can already take feats with Lessons of the First Ones, so there's nothing severely off about this, and this makes that final invocation feel a lot less awful as a cost. The Bladelock would thus be getting higher but slower power gains.
2. Rebalance existing full-caster part-martialist subclasses (Valor Bard, Swords Bard, Bladesinger, etc.), to offer a limited selection of Fighting Styles and/or Weapon Masteries. Perhaps see about letting them choose to give up some feature they currently get in order to instead get the Weapon Mastery feat for free (sans ability score improvement.)
3. I'm sympathetic to the "Monks should have this" angle, so perhaps give specific subclasses specific, rather than selected, options, and then a reworked Kensei can be the subclass all about properly integrating weapon training with martial arts? E.g. maybe Shadow gives you Dagger, Light Crossbow, and Quarterstaff, while Open Hand might let you treat your hands as though they had the Topple, Sap, or Graze mastery property (chosen after each long rest). IOW, keeping the choices flavorful and thematic, but also reasonably useful especially for the kinds of things any particular type of monk is likely to do.
4. Potentially rework the Fighting Style feats so that they require either having the Fighting Style class feature, or being at least character level 12. This would put them out of reach for pure single-class full spellcasters in most campaigns, thus preserving the effective "this is a martial feature" element, while still allowing very seasoned, practiced characters to work toward it at very high levels. It would also make sure that weird multiclassing dips other than those into Fighter/Paladin/etc. wouldn't specially advantage anyone, because ASIs are class-linked and if you've MC'd, you're unlikely to get a feat until 13+.
Beyond that, I think we'd definitely be diluting the value of Weapon Mastery and Fighting Style too much.
This would also, incidentally, be a great reason to create an actual Swordmage class. Y'know, one that blends full-throated spell-work with full-throated martial expertise from 1st level, rather than having to settle for being crappy at one side or the other for a long time....