One problem with even advancement is the first 6 levels - no ASI. Then, 7, 8, boom, 2. There's no excuse for that. Especially since advancement slows dramatically after 3rd, and campaigns rarely reach 16th, so you can forget that 3rd ASI. Going 4 of one (or 5 if wanting extra attack), 4 of the next makes oodles more sense given the arbitrary pegging of ASIs (& Extra Attack) to class level, even while 'fixing' spells and cantrips to advance smoothly on character level.
However, the dual-classing narrative is not nonsensical, at all. Changing careers is very much a thing, and includes character development. You start out a idealistic would-be hero, become a cynical mercenary, then find religion, for instance... Or, you start out as an urchin yearning to learn magic, but for many years only pick up tricks from other rogues & charlatans on the streets, eventually you convince a wizard to train you - or, in desperation, make a pact...
Would you as a GM have any problem with these multi-classes?
Why?
Any GM has some reason for trepidation about MCing, given it's history. TSR-era MCing was OP at low level, gimped at high, unless you ignored race/level restrictions (which was not uncommon, IMHO/X), in which chase it was OP all the way. 3e MCing, which 5e MCing closely resembles, was wildly abusable, sometimes even by doing some of the things you're talking about, so you could be 'triggering' your DM's 3.x traumas. 4e feat-based MCing was a freebie is you wanted an extra skill, a feat tax if you wanted to swap powers, and a complicated, mostly-underpowered/somewhat-abuseable ...whatever Hybrids were, exactly.
Personally, as a DM, I allow, but don't encourage MCing when running AL, because I have no real choice in the matter, and don't use it when I run (but I mostly run low-level, intro games at conventions using the basic pdf, so there's all sorts of stuff I don't use). When I finally finish my current campaign and start a new one, though, I don't have plans to use MCing - I have in mind a fairly tightly-themed campaign, and MCing isn't called for (specifically, the last time I ran a campaign like this, I allowed MCing, and the result was that the theme was lost in the impetus to create a 'complete party' using MC'd PCs, so, not this time).