It depends on how you mean that. If the dynamic you were drawing was “hadn’t voted for partition and had instead voted for one state”, then the same thing would have happened as the UN did nothing and never intended to, it just made some proclamations.
If you mean that the UN would have either enforced the creation of one state (and stopped Jordan and Egypt from gobbling up parts of it) or actually acted to create two states, then things would have been drastically different.
I’m not talking about any racist code, (although I’m sure that a non-zero number of those making the demand are racists). I’m pointing out that ending the state of Israel and creating a state of Greater Palestine, or what have you, is a backdoor method to simply ending the state of Israel. It’s not a “compromise” position, it was the demand of the Arab powers in 1948 and it’s still the demand of those who refuse to recognize Israel and still have maps with the entire area simply called “Palestine”.
Saying that we should effectively erase the last 60 years of the existence of a nation and just declare that the entire region is “Palestine” is, obviously, a demand that the state of Israel will be done away with. It’s, equally obviously, not a demand that there will be a state of Israel with roughly the same geographic boundaries we have now, and the same system of laws and government, but that state will be absorbed into another one. If, at no point during the last 62 years, the absorption of Israel into someone else’s country was palatable, why will it be now that they’re had a sovereign nation for more than half a century?
“We don’t want to end Israel! We just want the state known as Israel to end!” is, shall we say, less than convincing.
There have been numerous ‘damned solutions’ offered. The acceptance of the Peel Commission partition plan, the acceptance of the UN partition plan, the acceptance of peace along the armistice lines before 1967, ~96% of the Palestinians territorial demands with Final Status issues to be settled at future negotiating cycles…
Throwing up your hands and simply saying “well, gee, why isn’t it fixed!” is an abrogation of your responsibility to analyze the situation, not an analysis of it.
As for why saying one nation doesn’t mean abolishing Israel, of course it does. Both factions, Israelis and Palestinians, have wanted self determination for decades now. Saying that neither gets self determination is not a solution. Ensuring that they both do, is.