Honestly it wouldn't be the worst thing in the world. Try ketchup and pb and it would actually taste good, since it really is a jam. (Jelly if you wanna call that texture jelly instead.)
And jam on toast goes well with coffee and tea. So popping some straight in would be a nice sweetener.
I would definitely try this if I were mentally unstable.
Too bad a key ingredient in ketchup is vinegar, otherwise your point would make sense (same for Sriracha, which is what my mentality unstable self would add).
I imagine the salt in it also isn't a great add, and the tomato is neutral at best. There is sugar, so at least there's that.
There is an acidic touch in coffee, and many desire that. In fact I add pomegranate molasses to my coffee once in a while. Don't think it would be much if an issue. Same for salt, it'll be too minimal a flavour to matter.