Paintings are not incredibly useful because they're such an idiosyncratic assortment of odd, and sometimes unsettling, little pictures. Almost none have been added since the early days of Minecraft, making them seem like a bit of a holdover. Ideas for fixing them have been floated many times, but almost all of them have to do with allowing for custom paintings. And I see problems with that approach. In light of changes made in 1.14, here's an alternate idea for making paintings more useful.
(I'd speculate that the current devs have a similar attitude to paintings that they do to furniture--they'd rather we use our creativity to come up with our own decorations. But they did add features so that they could be placed more easily, so they do still seem to be supporting them. At any rate, hopefully this idea would fit with their general philosophy pretty well.)
Add Painting "Styles" - Just as village architecture now varies according to biome, villager paintings should do the same. Paintings created by the player would be the same no matter where they were created and would draw from the same pool of images they do now. But paintings obtained from villagers would actually be of distinct types, and which you received would depend on the the biome of the villager in question. There would be an "Arid Painting" (dessert), a "Pastoral Painting" (plains), a "Sublime Painting" (taiga), and etc. Thus, in order to obtain the new paintings, one would have to locate villages of the appropriate sort and then build trade relations with them.
Each sort of painting would pull from a different small pool of images in a style that would be at home in the village in question both in style and color pallet. Most new images should be fairly abstract, perhaps taking inspiration from real cultural art traditions. For instance, paintings originating from Savanna villagers would be reminiscent of African tribal art, those from snowy taiga would put one in mind of Scandinavian folk art, etc.
To support this new system, the cost of trading for paintings from villagers should be raised significantly. Also, it might make sense to add a distinct "Artist" villager, rather than getting one's art from the shepherd (though, if this is not done, at least it justifies the current, bizarre decision to make paintings the highest tier trade). An artist could have an easel for a workstation, and give emeralds for various colored dyes and for white wool.
One other, closely related idea: allow the artist villager to paint a "portrait". This could be the one nod to customizable paintings: a portrait would show the player's head in Minecraft's answer to classic portraiture. (Perhaps a full length version would be possible from the same item depending on where it was placed.) The appearance of the player would be taken from their skin, a file which the program already has access to, so no uploading of graphics or etc. would be required. It also wouldn't create any avenues for abuse beyond what exists already.