why don't we have them?

This was before I started (pre 2015) but I believe there were ILs on speedrun.com for Crash games but they were removed due to lack of submissions.

Most speedgames don't have them unless there's an ingame timer it seems.

One issue for this game would be global cycles, so if you wanted the ILs to be " fair" you'd have to have die before starting the timing or something and even then glitched cycles become a thing.

@Tebt_W i see... is that the same for crash 2?

I believe so yeah.

As for the Crash games that have time trials it looks like the remakes have time trial leaderboards here. Crash 3 I made a spreadsheet of every time trial WR and there's a couple websites with leaderboards. TWoC is similar but there isn't a spreadsheet with the WRs, same with stuff like XS and N-Tranced

@Tebt_W ok nice videos btw