The problem is mail servers. They usually don't support search this way, so the client has to download or cache each message to do the search. Gmail gets around this by having their own protocol and the indexes ready.
The quick filter finds messages in seconds in a folder with > 10000 mails. Not instantaneous, but not forever.
The global search is instantaneous because Thunderbird indexes the mails.
Not having to rely on the Internet to find your stuff is a feature, not a bug.
Snark aside, I sometimes feel like we reinvent the wheel using new technologies just because we like the new hotness.
I see the OS battles take place and my only thought is..at work, I want an OS that: Boots and then gets the hell out of my way so I can do my work. I don't want it to try and sell me things or re-arrange things or have to spend time tinkering or fixing it.
Now in my free time, sure! I set up a computer with pass thorough GPU so I can game in Windows while running Linux. It was fun and a learning experience.
Full-text indexing isn't dark magic at all.
Also most of it will be likely some bloat form HTML mail and attachments (especially with their inefficient encodings).
My point was: Handling full-text search indices over even dozens of GB of plain text isn't anything a mediocre computer couldn't handle nowadays.