Note that this is subtly different from the “one level in every class” thing; this is about taking your levels one at a time, starting from level 1, rather than a fully-finished level 13 concept.
Could this be at all viable? What order would you go with?
It’s interesting because you don’t want the level 13 end concept, so the question becomes how the power level compares to normal progression? Obviously the first level is the same since you can’t multiclass, but at some point this is going to drop way off. I’m not sure at what point.
I think the biggest problem is that you’ll have to be incredibly mediocre in all your abilities: even with +3 ASIs from race, point buy can only get you straight 13s, and while you could theoretically delay some abilities through ASIs, you pay extra in point buy past 13 (versus ASIs which are all equivalent).
You could probably set up an Eldritch Blast character with a bunch of utility cantrips, but making attacks with a +1 bonus is going to be agonizing, unlike your damage since you can’t take Agonizing Blast. You’ll scale with level but it’ll drop off pretty quick, since one level in lock keeps you behind on damage and you’ll never get the splashier spells more focused characters will.