Is that purely a matter of culture and norms, or are there rules that forbid it also?
There are no rules that forbid it. At lower-league (i.e. for teams below the Football League) level it actually happens all the time. There were also a few big clubs (Spurs are one name that comes to mind) who used to play reserve teams in the amateur divisions before those divisions were linked to the Football League through pro/rel about 50 years ago, too.
Theoretically it could happen right now if PL teams were to create a B-team all the way down in a county-level league, where the organising body would be far less picky about who they admit as a new team, because I guarantee you that if a B-team were to be promoted into the Football League rather than being placed there from scratch, they would be allowed in (there would still be disapproving mutters but they would likely be no more than mutters). Thing is, what team is going to invest in a B-team that will require 5-10 years of successive promotions before getting to a level acceptable for fostering youth talent?
No, the real stumbling block, basically, is that English (and to a lesser extent, British) football has a long and storied history of treating its Football League teams as the equals of its top flight teams - remember it was only in 1992 that the top flight separated off to organise itself in its own competition. That's not to mention that very few of the FL teams have any shorter a history than the big PL teams, and many of the teams in the lower reaches of the FL are the teams who, 100 years ago, were winning the inaugural versions of many of the cups and leagues which are now some of the biggest prizes in the game. If you just look in League One (the third tier) you can find cumulatively 14 FA Cups, a League Cup and a top flight trophy between them. If you look at the 12 teams that contested the first ever Football League season in 1888-89, only three of them now play in the PL (and for the record, they are all still playing football - none have gone out of business in 129 years). If you look at the list of top flight winners, fully 36 seasons were won by a team no longer in the PL.
These kinds of team may accept that they operate now on smaller budgets for smaller prizes, but they and their fans won't be persuaded that they are lesser clubs than those who now play in the PL. In fact, most will have considerable resentment for the teams in PL, and see the money in the game now as cheapening any accomplishments that PL teams achieve. In this kind of atmosphere, it's pretty much impossible to persuade these clubs and the league which organises them that they should have to suffer the indignity of competing against the reserve sides of those who have taken their places at the top table.