Really? How?
My expectation would be that extracting a subtitle file takes a few seconds at most. If you had to do it on the fly every time you watched anything in your library, it wouldn't matter.
ffmpeg -i input.mkv -map 0:s:0 /tmp/subtitles.srt
If I extract SRT subtitles from a 47 minute video, it takes about one second, so your two-hour duration isn't what's causing you to wait. You might be decoding two hours of extremely high-resolution pixels, but there's no actual need to do that either.
If the SSD was completely idle and could reach it's max rated read speed of 550 MB/s, assuming absolutely no overhead, ffmpeg would finish in just over 2 minutes (70000 MB / 550 MB/s / 60 s/min = 2.12 min). So, in the best case scenario, I'll be stuck waiting for 2 minutes for the subtitles to appear, if the client doesn't time out. Real-world speeds are 10x slower, as we've seen, but they're more than 10x faster than 4K Blu-ray bitrates, so they're sufficient.
How large is your 47 minute video? If it's ~8 GB, which is typically on the high end for episodes from streaming services, and if you have an PCIe 3.0 NVMe SSD, which reads at ~6 GB/s, you'll extract subtitles in about 1 second.