I don't doubt that VRAM usage is going to increase. After all,
software is a gas. I'm not the type of person who's ever really run a lot of older games with high-res texture packs, but I'll be honest that talking about Skyrim has kind of made we want to fire it up again, but I'm not sure if the progression to 16 GB will happen that quickly or if there's much to necessitate it.
Probably the best way to get an estimate of how soon we should expect it to happen is by looking back at previous progression as the amount of VRAM available on cards has changed over time. We haven't even reached a point of wide availability of 16 GB GPUs since they're only starting to trickle out just now. I suppose there are a few people who have had a Radeon VII or a Titan card for some time, but that's a tiny number of people. Based on current rumors most people who want any of the new cards in that class are unlikely to get one until March at the soonest.
When you bought a RX580 4 GB, you're talking about an amount of memory that would have first started appearing in high-end cards 5 years prior to that since Polaris 20 cards came out in early 2017 and the earliest cards to launch with at least 4 GB of VRAM were the first high-end GCN cards (7970 6 GB) in early 2012 and high-end Kepler (4 GB 670 and 680 models) a few months after that.
Over the next two years 4 GB would become more mainstream as the GTX 700-series had 4 GB options in cards all the way down to the 730 and AMD having the option available in all of their midrange cards and even a version of of the 240 that offered 4 GB. By 2015 4 GB was becoming the standard option as opposed to a premium choice and the move to 16nm in 2016 meant that you had to get down to the $100 product level for both AMD and Nvidia before you could even buy a card (let us not speak of the 1060 3 GB) with less than 4 GB.
I don't know precisely when the move to 8 GB minimum for textures occurred, but it was presumably sometime after you got your RX 580. Either way, we can just look at the adoption curve for 4 GB and see that it took at least 5 years, and probably closer to 6 before texture packs moved beyond that point and made it obsolete. I suspect that a large part of that had to do with availability and adoption of 4K resolution, but I don't see anything replacing that for a while still.
The lack of 16 GB in most Nvidia cards will also likely keep the progression from starting for a while longer and with the previous Ti cards being much closer to 10 GB than 16 GB, I don't think there will be as great of a push to go much beyond that. AMD's Navi 22 cards which will probably be in the $300 - $450 range and sell in far greater quantities than Navi 21 will have 10 GB and 12 GB variants which will further make that range a popular target.
But if you're looking to invest in a ~$700 GPU (well assuming you can get one at MSRP right now) then it's not wrong to want a little peace of mind that lets you know your investment will last you a while. Even if it just gives you a lot of extra room to cache textures so that you don't need to load anything from disk twice I suppose there's some benefit to it. Maybe talk to other people in that community or some of the people who produce the textures to see what their thoughts are since it's going to be a much more informed opinion.