Is this because Betamax recorders and/or tapes had the same sort of 29:59 limit that some cameras have today (e.g. cheaper Canons)?
Betamax was limited to tape speed and how much tape could fit in the cassette. It was one of the downfalls of Beta. It only recorded at one speed. VHS could record in 3 speeds SP (normal), EP (half speed doubling record time), or SLP (third speed tripling record time). At the end of VHS, they were able to create an extremely thin tape allowing for 180 minutes of SP time in the cassette. In SLP, that's 9 friggin hours of record time. It looked horrible, but people loved it. People were essentially running their own DVR with a programmable VCR in SLP with a 180 minute load. You had to fast forward/rewind to find your shows, but even commercials we being skipped.
In the beginning, yes. As time went on, Beta also offered three speeds (Beta I, II, and III) exactly as was offered by VHS and their three speeds.
Maximum recording time for Beta ended up at 5 hours on a single cassette (L830 cassette and Beta III speed). The L750 cassette was more commonly available, it recorded 4.5 hours at Beta III speed.
Of course, VHS's physically larger cassette always allowed it to have a somewhere longer recording time at every step of the competition.
Edit: Add link to Wikipedia page for Beta tape lengths and recording times:
An answer here https://photo.stackexchange.com/a/21181 says it's to do with codec licensing but the businesswire link is dead and I can't find anything else to back it up.
As time went on, longer cassettes and slower recording speeds were released and Beta recorders eventually had tape cassettes available that recorded for 4.5 hours (L750) or 5 hours (L830) of time on a single cassette.