This rule makes me laugh every time I hear it now.
I am not defending this rule btw but I maybe able to assist why it came about.
I first dealt texas hold'em in 1988, the games the casino offered in the cardroom were, Brag, Kalooki and Stud (Stud variants included 5 card, 7 card and Strip deck stud). Cardrooms in casinos were inhabited mainly by chancers and criminals and there wasn't many at the time that offered poker. Off the top of my head I could think of probably 1 legal cardroom in Birmingham, 1 in Coventry and 2 spielers, not sure about the rest of the country, but I believe there was only 3 other places in the uk that offered poker. Blackpool, Bradford and London and it was mainly 7 card stud.
I believe the game was introduced by a punter who had seen it in Vegas, and was introduced "As he remembered the game" being an avid stud player, can't remember his name but something in my head is saying Tony Sarancene? (maybe the fox will confirm?). But this was obviously way before the internet so the rules could never be checked lol but the rules were basically winged.
Dealers choice cash games were stud, draw, or brag but this game called Hold em kind of appeared.
A trial competition was introduced after someone decided to write a few rules down. And as Hold'em had grown through this dealers choice game the blinds were called Ante's and the button and left of the button posted them (they were a flat 25/25 no sb and bb), and the game proved popular. Punters moved from all over the country to be close to the Rainbow Casino. This sparked other local casino's to introduce hold'em within the year to attract the players to their casinos. Namely in order Rubicon Coventry, Sergeant Yorkes (later Rank then Grosvenor) and China Palace. There were 3 spielers to continue the game after the casino's closed at 2am!! Louis the Greek, Barries (chapter about it in Swimming with the Devilfish) and another that I can't remember off the top of my head but it was an Asian with an English name lol. ALL of these places used the rules from the Rainbow as it was the only point of reference. (in Birmingham anyway, not sure about the rest of the country).
Back to the rule of leaving the table lol.
I will probably get shot for saying this, but as previously stated the kind of player that played poker was usually a bit naughty and sitting at a poker table was like being in no-mans land. It was very bizarre being a dealer then as all sorts of crimes were openly discussed at the table, but at the table was honour amongst thieves, every one was polite and there was no such thing as speech play. In fact any reference to your cards or others was considered unethical and outlawed lol.
The casinos made their money from poker players on the house games as they were the players with money, there was no such thing as registration charges and poker players were looked after. Breaks in a tournament were regular and long so that the house could get their hit, TD's were regularly told to extend their breaks and often didn't restart until all players had returned to the cardroom!
It was considered very rude to leave a table or not return due to the players mega role on the dice table, and it was actually the bigger poker players that thought they should be penalised for not being at the table and so after pressure the rules used to state that after 3 hands a missing player would have to post an "ante" and it should have been doubled for every hand thereafter. But it was a disadvantage to the house for this rule to be implimented as they wanted the player to be on the house games
As staff moved from casino to casino, this rule was diluted along with others. Another irregularity that transpired from this period is the betting amount.
The Rainbow's rules stated that a minimum raise must be double the total call, which has caused problems up until this day and is still used in most cardrooms in Ireland. The reason for this is that the Rainbow used to hold a big comp called the British Masters and they had an agreement with the Merrion that they would swap staff when needed for the bigger comps and they also used the Rainbows rules.
It wasn't till the introduction of the internet that other "proper" rules were followed, some places/people adapted and put up with the arguments from the locals that they had been playing the wrong rules for over ten years, and some places/people didn't. It is the *bleep* ones that knew the rules were wrong but didn't adapt fully and picked and chose the rules they wanted that seem to cause the problems today.
This is just my experience any old timers feel free to correct

The team that opened Star City were the old rainbow lot including Zac and Bonnie(rip)