Ukraine

While I agree that they are old and obsolete by our standards, there are navies out there still using them. I think Australia even has a couple. They have even upgraded the missile system to fire a multitude of different missiles, including the SM2 and Tomahawk. These ships also have Harpoons aboard. Remember that UKR doesn't have to roam the open ocean and project power globally, they just need something for the Black Sea to protect their flank. The radar systems are all out of date, which makes me feel really old because those are the radars I cut my teeth on, with the 49 air radar, the 55 surface radar, and the slick 32 EW suite, but again, I think they would help in the Black Sea.
Ukraine will need a navy as they are not land locked. The only other thing besides old, out dated, frigates would be something comparable to our Coast Guard cutters. If Ukraine's infrastructure could eventually handle the upkeep, I see no reason why we can't just give them about 3 or 4 Perrys to roam their coastline.
I like your arguments.

There's one of my arguments which still stands. They have been sitting idle but not having been properly mothballed, for about 10 long years. They can be fixed up to be used again, but I would estimate that even a fast program to do that kind of overhaul would take 1 to 2 years.