Rigardi comes from the Romance languages. Following the pattern in French, Italian and Spanish one would say rigardas la televidon, for watching television and I think many Esperantists would say just that.

Also, I think many Esperantists would say mi aĉetis novan televidon/ radion meaning the aparato.

Television isn't enough of a spektaklo to warrant spekti la televidon in preference to rigardi. In general one spektas some sort of event, though you might say spekti filmon or vidbendon.

You might also say mi spektis la ceremonion en la televido, and in English your might use either I saw it on the telly or I watched it on the telly, but never 'to see' for watching television.

Television isn't enough of a spektaklo to warrant spekti la televidon in preference to rigardi

You're probably right about 'rigardi' being fine for this, however I don't think spekti is wrong, or even evitinda. Possibly this is more modern usage but I see and hear it used quite a lot for televido. There are also some Tekstaro hits in Monato and La Ondo. Google has about the same number for both spekti and rigardi. The Vikipedio article for 'televido' uses 'spekti'...

I would also say that if "spekti filmon" is fine - and it must be since it appears all the time - then "spekti televidon" ought to be fine too since that is the format the majority of films are watched in. It seems a bit arbitrary to say that somone 'spektas' when they happen to have Netflix on, but when they switch over to a soap on BBC1 they only 'rigardas'.