It wasn't just getting the monitor refresh rate working.
I started using 3D acceleration when Compiz/Beryl was released (2006) with an NVidia card. I was playing World of Warcraft under wine at that time too. The only problem I had was when I updated the kernel I had to remember to recompile the drivers under Debian. I switched to Ubuntu for that reason (because then I didn't have to do anything).
Eventually I retired that and went with an Intel board. It worked 100% but was dog slow at the time (pre-2010 Intel drivers were quite good at 2D acceleration but abysmal for speed at 3D). Compiz worked perfectly, the only problem was a pretty big hit in frame rate for WoW.
I replaced that with a Radeon Card which worked perfectly under Catalyst. I started hearing rumours that the free software drivers were getting good performance numbers and switched to that. 2D was amazing (dramatically better than Catalyst) and 3D was slightly slower, but comparable.
Finally replaced that with a few laptops running Intel hardware again. By this time (2012) the 3D performance had dramatically improved and I'm quite happy with it. Obviously not a gamer set up, but more than adequate for casual gaming.
Before 2006, I think you were pretty much stuck with Nvidia and proprietary drivers if you wanted 3D. Again, I never heard anyone who had real problems other than recompiling the drivers if you were on a distro that didn't do it for you.
I actually worked with Gavriel State at Corel before he started up TransGaming. I thought he was completely nuts to do it because at the time there was almost nothing that ran under Wine properly. That was 2001. Honestly, if you were trying to get 3D working on Linux, you were mostly doing it just to say you did it.
I'm not going to deny that some people had problems with video cards. I often had to jump through hoops to get random hardware at work to give me nice displays. But if you were careful to buy supported hardware, there were very few problems.
To be fair, I did a lot of Windows development in the late 90s and early 2000s and I had at least as many problems with video drivers under Windows. The difference was that on Linux I would have trouble with new hardware, while with Windows I would have trouble with old hardware. The other big difference is that with Linux, you could almost always get something to work so that you could hack on it. With Windows, getting to a point where you could download updated drivers could be unbelievably painful.
It is quite possible that one had to still edit modelines by hand at that time, but it really wasn't long before the modeline db came out and you could just plonk in canned values with a good expectation it would work untouched. Certainly after that time I never had any difficulty. About the only thing I ever did was to follow instructions to modify a couple of numbers for monitors that had bizarre refresh rates.
I think that this would probably fall pretty close to the "20 years ago" time frame (August 1995). Slackware 3.0 came out in November of that year. 2.0 of the kernel came out in 1996 and I'm quite sure that I wasn't spending any time editing modelines then.
If you wanted to get total plug an play without any configuration at all, I think you would have to wait until 2004, when Ubuntu was first released. So while the original statement that it took 10 years to get video drivers working is completely wrong, I think it would be fair to say that it took 10 years to have an equivalent install experience to Windows on that front.