Well, the ERA wasn’t “just for women”. It would have prohibited discrimination “on account of sex” and, obviously, men could take advantage of that as well as women.
But, more to the point, there’s already a general equality provision; under the 14th amendment, no state shall “deny to any person within its jurisdiction the equal protection of the laws”.
In one respect this is broader than your proposal. It doesn’t depend on citizenship or the right to vote; it applies to all persons within the jurisdiction of any state, including minors, foreign nationals, etc. (This seems to me appropriate, if we believe that human rights inhere in people because they are human, rather than because they were born in this location rather than that, or because they happen to satisfy the suffrage qualification of this particular state.)
In another respect it is narrower. It doesn’t affirmatively confer rights on people. It negatively restricts the states from denying equal protection. But a state which affords no legal protection at all to a particular right is not in breach of the 14th amendment.
The constitution itself confers few rights but those which it does confer it confers on all citizens, or on all people, so your formulation would have no effect as regards constitutional rights. It might have some effect as regards rights conferred by legislation, but not necessarily the effect you want.
Consider; state law confers upon X the right to drive on the public highway. Should the state therefore be obliged to confer the same right on every voting citizen, regardless of competence, fitness or past driving history? Just because we don’t consider sex a relevant ground for discriminating between citizens doesn’t mean that there are no proper grounds for discriminating between citizens. Competence to drive is a perfectly proper basis for discriminating beteen citizens when it comes to issuing driving licences. Thus a constitutional prohibition preventing all discrimination on any grounds whatsoever would be madness; what is needed, if anything, is a constitutional prohibition preventing discrimination on grounds which society considers arbitrary, invidious, offensive . . . [insert adjective of choice here].
The constitution forbids discrimination as regards voting rights on the grounds of “race, color or previous condition of servitude” (15th Amendment) or “failure to pay poll or other tax” (24th amendment) but does not otherwise enumerate forbidden grounds for discrimination. And even these provisions relate only to voting rights. For the protection of other rights, or to fight discrimination on grounds other than race, colour, etc, there is nothing but the 14th amendment, whose language is . . . flexible.
The case in favour of the ERA, I think, would have been something like this.
Discrimination on the grounds of sex is widespread.
It is offensive.
Therefore it warrants a constitutional prohibition.
Part of the case against it was that such discrimination was not, in fact, offensive. But another part was that the equal protection clause of the 14th amendment was a sufficient foundation for legal prohibition of arbitrary or invidious discrimination. Obviously, the case in favour of the ERA wasn’t strong enough to command the necessary political support to have it ratified.