The advantage of home-made food is that you have control over the ingredients.

Store bought mustard and mayonnaise contain such surprising ingredients like e.g. sugar or copious amounts of salt.

While I broadly agree with this, I would say that my own attempts at making mint sauce were fairly disappointing in comparison with shop-bought - Colman's mint sauce is an awful lot nicer than anything I was able to make, and (though I've never tried to make it) I bet their wonderful mustard is too.

You will probably also not be able to make at home anything all that similar to the mayonnaise you buy in a shop, though what you can make at home will almost certainly be equally as nice (my children were confused by the yellowish colour of home-made mayonnaise, which is sort of backwards since the confusing thing ought to be why shop-bought mayonnaise is white!).

What store bought mustard contains sugar? I'm not aware of any, and if there are, they aren't common.

Also a little bit of sugar in mayonnaise is fine - in the US it usually relatively trace amounts to the most commonly sold ones in the Commonwealth.

Another advantage is that making your own x from scratch is fun and satisfying. Mayonnaise, mustard, soda, barbecue sauce, gravlax, liver sausage — it's fun to see the things people buy ready-made, and know you have the knowledge and ability to do it yourself. Sometimes it's enough better to be worth the effort; sometimes, like catsup, you find that the store-bought is better — but you still have the fun of doing it and the satisfaction of knowing for sure.