That is not a solution to the problem "class design is severely constrained by multiclassing." It's an example of the problem.
Furthermore, it misses the larger picture. The existence of a handful of overpowered MC builds is one part of that picture. The other part is the vast sea of MC builds which are painfully sub-par compared to single-class. Multiclassing on the 3E model has never worked well. It's a trap for novice players and a tool of abuse for veterans.
I've said this before, but it bears repeating: 4E was the only edition to get multiclassing right. For those who just want to dabble in another class, offer feats to cherry-pick the features you're after (5E has also started providing these). For those who want to fully combine two classes, take each class and create a "half-version" of it, such that you can take two half-classes and glue them together to create a hybrid whole.
