Does the idea that women want relationships more than men because of evolution make any sense?

I tend to think it has more to do with social constructionism. That is, it's a social construct -women are told/shown (through example, often) from an early age that they should and will want monogamy, that that's the proper way of expressing their gender and sexuality, and that they should be ashamed to want anything different.

Men are told/shown from an early age that they should be proud of their sexuality, that sex is a conquest, that they should avoid being 'burdened' with monogamy.

Evolution may play a role as well, but it's not just evolution. Our behaviour is more than our biology.

Evolution works on the principle of natural selection, according to which traits are selected for when such traits enhance survival of the species. If males "bolted" in primitive times it was either to hunt and provide for the family or to impregnate other women. In either scenario, survival of the species was enhanced. The masculine role was not to stick around with the children. The masculine role was to exhibit promiscuous sexual behavior and aggression (in order to succeed in hunting and combat). It was the feminine role to stick around and nurture the children. Both masculine and feminine roles enhanced survival of the species and are thus consistent with the theory of evolution.

It does seem to make sense on some levels. There are a lot of other social factors that contribute to this argument, though.

If one male has 400 mates, and the other has 1 but provides for the offspring, who do you think will likely have more reproductive success?

Evolutionarily speaking, he is bolting to find a hotter chick to breed with and have better looking kids with who will survive.

As they don't have physical power or brain power, women had to develop other sources of power or risk being extinct.

Love was created for the benefit of females.

Female beauty " "

Sexuality " "

And male lions eat their own cubs.

Yes it does. You just explained why