The English League System was established in 1888. The Irish and Scottish Leagues were formed in 1890. The FA Cup was started in 1871/72(albeit with Scottish teams competing in the early years and indeed Queens Park making two finals), the Scottish Cup began in 1873, the Irish Cup in 1881. The only exception is the Welsh League which was established in 1994. The first thing is that there are huge reserves of history you would be tearing to bits by creating a unified British system.
In the early years, there were good geographic reasons for this, but rivalries gradually built up inside the league structures and the systems became entrenched. The international rivalry created through the Home Nations tournament also helped develop interest in the sport. The separate Home Nations, subsequently opening up to other nations are one of the main reasons for the development of the sport.
Again you are ripping this up for no good reason.
Scottish club football is in a similar position to many smaller leagues. The days when the historically big clubs in Europe like Rangers, Celtic, Ajax, PSV, Brugge, Rapid Vienna, CSKA Moscow, Porto, Benfica, Sporting etc. etc. can compete with the top five leagues on a fair basis is dead. This is entirely due to TV money. It has given fake plastic wankers the impression that teams like Huddersfield are a bigger club than Ajax or Celtic.
The trick is to find a way to restore parity somewhat whilst not destroying the league systems.
Whilst Celtic would be helped financially by such a move, I fail to see how it would help the likes of Aberdeen(who have won two European trophies in their history) who would be stuck for the foreseeable with trips south of the border would dominate their fixture schedule and away support likely drying up for geographic reasons. It would make no sense and assuming they would be in the Championship would hurt them financially.
Further, you have clubs at the lower end of the EPL who would be unhappy at Scottish interlopers, either through promotion or through placement. Either way, it would increase their chances of being relegated. It would not be something that would be welcomed in any way.
So it wouldn't benefit the non-Old Firm teams in Scotland, it wouldn't benefit the lower level English teams and possibly over time given the size of the OF Support could also affect the larger English teams.
Nobody would benefit.
Moving on from Scotland, whilst the Scottishness of football would be diluted, domestic football from Northern Ireland would be demolished. Their league is small, it is part-time but it is something that is
So, you would see two leagues of nearly 130 years vanish in fact, one of exactly 130 years technically go. You would likely see two national cup tournaments vanish, one(the Scottish Cup, which currently uses the oldest sporting trophy still in use in the world). You would destroy football in Northern Ireland. You would harm football in Scotland as teams would be shoehorned into the larger English system. You would harm clubs in England, relegating teams through no sporting reason.
Could a Team GB work? Yes. Should it happen? No, no, never.