Counterstrike, as another commenter pointed out, is still the third most popular game on Steam. And yet, every major FPS franchise has moved further and further away from that model.
SOCOM and the Gears of War franchises were probably the two biggest non-respawn online shooters on consoles, and the latest iteration of both has instead put respawn pandemonium front and center instead.
Nothing beats the tension of a shooter where you don't pop back to life 0-5 seconds later. It makes players more likely to work as teams, and it compels players to act with self-preservation instead of running around like damn fools.
I miss those experiences. Hell, I'm playing MW3 because Search & Destroy mode is the closest I can get these days, outside of hardcore PC games like ARMA (which I would probably love if it didn't run like garbage).