Replace the 「あるのみ」 part by the other words you mentioned and these phrases will lose the nice literary and/or old-fashioned 'feel' that was intended by the author/speaker. In other words, one should not try to make these phrases look or sound unnecessarily more conversational.
「[Noun] + あるのみ」
should be left alone as a common fixed expression used in mottoes and slogans. A strict grammar analysis would be somewhat fruitless because the expression already lacks the important particle 「が」 between the noun and 「あるのみ」 in the first place.
「ある」 here simply means "to be" or "to exist". This verb choice is completely acceptable and totally natural for the expression because what it literally means is:
"Let there only be [Noun]!"
which in turn means:
"The only thing to do is [Noun]!"