My feeling is that in the beginning, all the wizards got to be Lords

But if everyone is a Lord, then for practical purposes nobody is. You end up with a Too Many Chiefs, Not Enough Indians situation. A Lord needs to be able to have servants.

It's important to remember that the Statute of Secrecy was only established in 1692. The family tree of the Noble and Most Ancient House of Black goes back to the Middle Ages.

Noble wizards / common wizards is unlikely to be the relevant demographic proportion; it makes sense that wizards would be disproportionately represented in the peerage.