Only if you will be in this house for a very very long time and will always like painted tile.
Basically, it sounds like you want things to look nice. That's great.
If the tile is considered a 3 out of 10 on looks why switch to painted tiles that will maybe make it 5 out of 10 at best.
There are paints that will adhere to tile. HOWEVER when bumped the paint scrapes off versus on a wall it usually smushes in for the most part and you have an indention that is painted.
Now there are recoating services that will spray on paint/"fake"-epoxy glaze. These look pretty good and the good companies have perfected these to perform well. These are all one color and if you are OK with that, that is a great option. Costly but this will look way more professional than a paint DIY. (I am an advocate of almost everything DIY, this the consumer options simply look horrible and don't work)
The other gotcha I have is if there are indentions on the artwork on that tile, it may not look well reglazed/resurfaced. I would vote heavily against anything if there are any indentions/raised parts of the tile.
Last thing. Value your time and money. Painting it will cost time and money. If retiling it costs a little more time and money then do that. If you are going to eventually retile - do it first. Retiling isn't hard since if the tile is laying flat now it is on a good tiling substrate. It isn't hard removing this tile and putting up new stuff.