Going by the popular vote isn’t going to fix the underlying problems with the first-past-the-post system.
No, but the electoral college is a problem that can be fixed without a constitutional amendment.
Such a fix is a workaround, not the true solution, and I’m not sure I favor workarounds. I’m pretty firm in my conviction that if the Constitution isn’t working in some way, then the Constitution should get fixed instead of finding loopholes. Unfortunetly, the Constitution may be just a tad more difficult than desirable to amend.
The National Popular Vote is one workaround, but there are other things that I’d classify a lot closer to actual fixes which also do not require a Constitutional Amendment. The NPV is merely the method that, at least at the moment, is most likely to succeed.