Why don't we have video recording of runways takeoffs/landings?
Because video is mostly useless for investigation.

The investigators need to know the exact flightpath, which is already recorded by the ATC radar and by the flight data recorder, they need to know whether and which systems failed, which is recorded by the flight data recorder, and they need to know what the pilots were doing, for which they have cockpit voice recorder and the radio communication is also recorded in the ATC facility (tower).

Video would be worse for determining the flight path than both ATC radar and FDR and while ATC radar does not have attitude, FDR does and again more precisely than video. Plus video might, depending on angle, have external damage, but that can generally be determined by examining the wreckage quite fine.

So video would add very little information over the existing recordings and thus it is not cost-effective to add it for just this purpose at all airports (it may be used if it is installed for security purposes).