I'm not sure what there is to be gained from dual classing that the existing multiclass rules don't already cover. Isn't dual-classing basically a more restrictive version of modern multiclassing?
If this is about the level cap, why not just use a house rule to do away with the cap instead of introducing this whole new (old) system?
5E multiclassing is so very much like 1E dual classing, I'm not at all sure what system you are actually proposing.
Not really.Dual-classing both used a cost by class-level mode.
So, Human Fighter makes it to 5th level, and takes the several years downtime (yes, that's buried in the rules) to become a wizard, he's now an XP0, but somewhere around 30-40 HP, level 1 wizard, who saves as the better of Wiz 1 or Fighter 5. He then adventures to level 5 as a wizard, and now can wield swords without penalty, and cast magic, but can't cast in armor.
Umm... no. Per Chapter 6 of the PHB, 5E multiclassing is like 3E multiclassing, not 1E's dual classing.
Would you allow 1E-style dual-classing in 5E? If so, how would you limit it? Allowing someone to dual-class from 1 level of Barbarian or Warlock to Fighter seems a mite good. OTOH Ftr 12 / Wiz 20 seems much more reasonable.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.