You pointed to something obvious, which is, in a 1:1 system, if pairing isn't perfect, some people remain single.
I agree. Some people will be single. That’s true in any system.
Polygamy is flawed too.
Say, in a polygamy, 1 man has 3 women as his partners, that would mean 2 men are single. You didn't remove singleness, you just increased inequality.
And we need to be realistic, attraction is selective, and compatibility matters.
Even with a perfect 1:1, you would still get singles because not everyone wants each other, and some choose to stay single.
Furthermore, singleness is not a flaw of monogamy, it is inevitable, and dependent on choice, preference, and competition.
Lastly, if everyone is forced to accept any partner, their individual choice is removed. That turns relationships into forced rigid distribution system than voluntary connections.