I don't know the rules about UK, but in US...
There's no comparison between the UK and the US where immigration is concerned. The USA has a well organized and regulated system that is professionally run and works like clockwork. The UK is a whole different story. It is very difficult to immigrate to the UK or get a permanent residence permit. The whole system is set up to be complicated, painful to navigate, and to deter you at every turn. Many people have given up in disgust when confronted with the deliberately obstructive and impenetrable bureaucracy involved.
While I'd say that the US and UK governments are very much kindred spirits, your description of the US system is absolutely batshit crazy wrong.
It's a mess. Applications taking inordinate amounts of time, all kinds of irregularities, etc. If you're living in USA, then you have no idea how US immigration is viewed by foreigners: these days, they only bother trying to move to US as a last resort. The hassle isn't worth it. It's easier to do Europe (including UK) or Australia.
And for long-term green card holders, the process to get US citizenship is taking forever now. We're talking about it taking 10 years to have applications processed. (Not 10 years until you're eligible to apply, 10 years from the time of application!!!) The backlog is unbelievable.
So while the UK does have a strict immigration system, and one that sometimes makes (serious) mistakes, the US system is almost indisputably worse.
(I'm an American living in Europe, and know various Europeans and Americans who've moved to the UK, as well as some Europeans who've moved to USA. And of course tons of people from all over the world who've moved to Switzerland. Switzerland is strict, but efficient and generally fair. USA and UK are both irresponsibly bad.)