Yes, this was indeed a common practice. So - let's step back to 1963, when Doctor Who first aired on television. Television has existed in various forms since the 1920s, but in the UK and the US, the format really increased in popularity in leaps and bounds in the 1950s, especially with the postwar prosperity of the US - this is when it recognisably becomes TV. UK television got a big kickstart with the broadcast of Queen Elizabeth II's coronation in 1953. Australian television went on air with the Melbourne Olympics in 1956. In the late 1950s and early 1960s, you really start to get staggering amounts of people watching the same program at the same time (e.g., the 73 million people in the US watching the Beatles on the Ed Sullivan show in early 1964).

At this point, however, people did not understand television as television, in quite the way that we would now understand it. They basically still saw it as a visually broadcast version of other entertainment media, and it took a while for people to understand its specific potential (similarly, it took people a while to understand that a vinyl record was an artifact in of itself, and not simply where the recording of a live performance resided). Often television shows in its early years were based fairly straightforwardly on formats from radio, or from the theatre, starring the same people who had hosted those shows on the radio or on the theatre. For example, Ed Sullivan - the host of the Ed Sullivan Show mentioned previously - had hosted live vaudeville shows in the 1920s and 1930s, before hosting a version of those shows on the radio.

It took quite a while for people in television - especially the people in charge of British television - to understand that people might want to watch a recording of a show again. The executives in charge of the BBC, broadly speaking, were older, and quite conservative, and had old ways of thinking. At this stage, most television was still basically broadcast live-to-air. Where people enjoyed a show, and wanted to see it again, the dominant institutional response at the BBC might have been to simply stage it again with a new cast of actors (or maybe the same cast). The idea of repeating a broadcast by replaying the recording was quite foreign to the way of thinking they had about television - and it wasn’t just the executives; the actor’s union would obviously prefer the BBC spent more money employing more actors (something that won’t happen if the BBC just played repeats). Rumours suggest that the BBC possesses a copy of the early Doctor Who serial ‘Marco Polo’ but can’t do anything with it, because the actor’s contracts of the era simply didn’t cover the possibility of rebroadcasts of the show, and that an actor who appeared in ‘Marco Polo’ (or their estate) wants a large payment to permit them to use their performance in a commercial way. The rumour may or may not be true, but it goes towards the overarching point - television was very rarely repeated in this era. And if that’s the case, keeping an archive of all the footage - an expensive proposition - wasn’t necessary. Especially for light entertainment and children’s TV!

In terms of repeats of Doctor Who, one very unusual thing happened with the very first episode of Doctor Who, ‘The Unearthly Child': it was repeated a few days later on the BBC. This occurred because the debut episode of the series had the misfortune to be broadcast on November 23rd, 1963, and got overshadowed by JFK's assassination. So the BBC decided to play it again, because they’d invested a lot in the program and were very keen on ensuring its success.

Otherwise, it took until 1981 for the BBC to broadcast a repeat of 'The Unearthly Child' - the iconic first episode of an enormously long-running series, one that a TV movie has been made about the making of. In a world of cable television, we think of repeats as being part of the core of television, that you can turn on a channel and probably see an old episode of The Simpsons or Forensic Files at any one time. However it wasn't until the mid-1970s that the BBC otherwise started ever repeating episodes of Doctor Who, and in the 1970s this was pretty sporadic. It really wasn't until the rise of commercial VHS tapes (and cable) in the 1980s and 1990s that most British fans saw old episodes of the program if they were too young to have watched it at the time (or missed it one night).

But - to get back to the ‘television being just jumped-up theatre‘ thing - the extent to which 'The Unearthly Child' itself (and most Doctor Who episodes especially in the Hartnell era) was more or less recorded live is underestimated by modern fans. Because of the relatively primitive recording technology of the time and the actors of the time who were very used to performing in live theatre, it was easiest to simply record an episode live, with occasional filmed scenes dropped in to hide transitions between sets, etc. It was pre-recorded, but really not that far off being a live theatre performance.

As a result of the jumped-up-theatre mentality, the fact that the BBC even has any footage of things from the 1960s at all, in a lot of cases, was not because they kept the videos/film canisters they used in the broadcast, but largely because they sold the footage of the shows onto other broadcasting networks around the world (a market that had only quite recently emerged, of course - the BBC also broadcast film footage of, say, American shows like I Love Lucy). In terms of Doctor Who, the footage of Doctor Who episodes that now survives often does so not because the footage was kept by the BBC but instead because film canisters holding the footage in Australia, New Zealand, Singapore, or Nigeria (etc) were left in a dusty room and forgotten about after the broadcast occurred in that country (or because collectors had gotten access to the footage somehow).

While old missing Doctor Who episodes being found is a big news item, given the show’s continued prominence, archivists have also found missing episodes of other shows (which also illustrates the broader point of shows not being retained in the BBC’s archives that I was making earlier). Recently, for example, it was announced on the BBC that an archivist, Phil Morris, had uncovered missing episodes of Morecambe and Wise, Steptoe and Son, and the Basil Brush show, for example.

But yes, plenty of what we'd now consider important British shows are either lost, or only partially available - the BBC saw much of what it did as fairly disposable light entertainment, that it didn't expect anybody would care about in a year, let alone 50. It didn't have the mindset that this footage would come in useful later, because nobody at the BBC in 1963 was really predicting a DVD market, let alone a streaming service like BBC iPlayer or Netflix. As a result, much of the footage of Top Of The Pops from the 1960s (featuring a whole bunch of now iconic British rock bands) is missing, likely lost forever. Plenty of comedy shows from 1960s British television are also lost - for example, one black and white predecessor to Monty Python, titled At Last The 1948 Show, featuring John Cleese and Graham Chapman and hosted by David Frost, for a long time only had two known episodes from two series (though recoveries by archivists have increased that more recently). Etc.