Male here. (Full disclosure I'm currently single and not in a relationship as of this writing, if you think that affects my answer in any way.)
This has been touched on by other responses but I think there is a subtle but very crucial difference between "X is important because it is the only thing I need in a relationship" and "X is important because it is one of many things I need in a relationship".
As a side note, I think it is very difficult for a lot of men (I am no exception in the least) to describe and couch their own needs in ways that the women providing those needs would be sympathetic to.
Regarding the first part about food: For people in my age/geographical group (20's, urban area) I think the belly thing is a bit less of a concern. Cooking has become both more of a universal and aspirational life skill what with the rise of foodie culture, food network, youtube cooking channels, and all that. Something I find darkly humorous is that if there is one thing that hardcore feminists, redpiller pickup sites, and normal people actually seemingly agree on, it's that 21st century men should know how to properly cook if they want to consider themselves a success in life.
Don't get me wrong, I certainly wouldn't complain if my potential girlfriend/wife/partner was a great cook and actually wanted to use those skills for me and our relationship, but it isn't something I would consider a must-have. I suspect that in an increasingly large number of places in 2019 there is too much sturm und drang and historical baggage around women's and gender roles in society to publicly say (regardless of whether or not you actually want it in your heart) whether you think it is your girlfriend/wife's responsibility to cook for you as a man.
Sex is a bit thornier though. I agree with the gist of many of the responses- I can get empty balls very easily (speaking as a single man). But intimacy in a relationship with another living, breathing, non-fantasy human being is a whole nother beast altogether. Another thing both the third-wave feminists and redpillers of the internet seem to agree on is that you can never compel or force someone to feel desire for you (though how their philosophies address this life fact wildly diverge).
And I think this is a much more salient point because, by and large, in a relationship, you can get a lot of your physical and emotional needs fulfilled by other people. You can have close, fulfilling relationships with people who aren't your spouse (like your family or friends), with conversations, party invitations, outings, and things like that. You can have friends and family cook for you or go out to a nice restaurant. But if you are in a monogamous relationship and you try to get sexual intimacy from someone else who isn't your spouse, we have a word for that, and it's called cheating.
I don't think it's my girlfriend's/wife's responsibility to "keep my balls empty", but it is undeniable that the sexual intimacy I receive should go solely through her, and trying to articulate this in a way that doesn't sound patriarchal or antagonistic is something that I frankly struggle with.