From what I recall, a combination of factors.
!: It's better PR than killing or jailing all those people.
2: It cleans up their streets of the 'unwanted'.
3: Each country was trying to colonize the new world, if there are people who actively want to leave, by giving them a place to go under british rule it just expands their power, and improved their international standing among other european countries.
4: At the time, it supported British trade. The colonists would send raw materials to UK, buy full materials, pay taxes and tariffs (i think), and probably a couple other things that I don't recall that also boost their economy. There was a word for this, and I remember my middle school teacher focusing on this as one of the main issues, but I can't remember the word.
There may very well be more reasons, but those are the ones that I remember being told. That first one may have just been a joke from one of my teachers though.
No your first point isn't a joke at all ...but there was more than the PR behind it
the rest of your points esp 3 is spot on ....however it backfired as the people they sent or forced etc well they were from parts of the UK that were ummm not exactly overly supportive of the Crown (and esp at the time of your War of Independence being that not that long before there was the last of a series of rebellions here, and incidentally there was a story circulated over here that there was a Crown offered to Charles Edward Stuart but he declined said ....probably because he was drunk at the time and also his english was almost non existent lol)
Another thing among many you may know is that your declaration of Independence does infact bear some very significant resemblances to one that was written over here but a heck of a lot earlier over 400 years earlier and I am not being nasty in saying that or trying to be ignorant )
The thing that I have encountered and my daughters still do is the word Scots-Irish .....there is really no such thing at all lol you are either one or the other lol not both , The scots-Irish as they are called are nothing more than Protestant scots that left Ireland (mostly the north, ie Ulster and they were only there as they had been forced there by the crown and then after the famines they or alot left ...ok some may have been born there so really they were Irish as such but very few Protestants back then would say that lol but thay another story and really in most ways doesn't concern, well sorta, but lets not go there lol
Even the General that fought for the crown Cornwallis was not of the first division by any means and the troops he had were ummm well how say we say not the best by any manner of means (no I'm not saying that to defend Cornwallis in any way ) the best of the best were somewhat busy elsewhere with other troublesome folks we had to deal with who were closer to home. Couple that with German Geordie thinking he knew better and that as I said a miscalculation had been made in who was sent there to "colonize" (ie Scots would not have faced scots ...regular front line highland regiments in the order of Battle would not have faced other Scots as they would have been their kin and well that would or could have caused mutiny) all mounted up to a disaster waiting to happen. It was also mooted that really the States were really to big to actually govern and India was a better bet and was the focus really and well it did go on to become the Raj, even there when "Britain" withdrew and partition happened that was in many ways orchestrated to cause trouble (controversial yes ) as ......well let them fight it out among themselves and it then means they won't bother us lol ...well until they need something and that kinda bore out lol, sorry that another story lol
Even your Civil War .....had Mr Davis accepted the offer of British Troops then there would be two "Americas" and he refused our Queen . He thought oh no they want to recolonize and that really was not the reason at all lol ...the real reason was that we wanted to split the continental USA as in two halves it weaker than in one whole, that together with our Queen at the time did not like Mr Lincoln at all ...but I am sure that some or most will disagree with what I have said but believe in this Britain is a master above all others in playing things and putting things into place like no other lol , and we do have the experience of doing so ...oh yes we have made a heck of alot of mistakes ....we learned from them though.
Even the way things are done now ......send a Carrier battle group to sit of somewhere or even when Japan was opened up by Perry lol......that was a thing that we did long before and it was called Gun boat Diplomacy (Palmerston did that as did many others to lol)
Not being cheeky but many many many things that the USA does us over here do look at at times and say yup we tried that and nope it didn't work then and won't now either. We even tried being a Republic and found out that nope that didn't work as the power goes to peoples head .....better to have someone above that that can (and genuinely the Monarch can, although I doubt they would, over ride the Govt, and I would suspect that for me any way that if it got that bad and the Monarch did step in then I would follow her banner as opposed to any politician, infact I spent a long time following her Banner lol , as we do not swear allegiance to the flag we swear it to the Monarch and there heirs an successors (yes Tez there ids more to the oath that you I and many others have taken when accepting the Queens shilling but lets not complicate matters lol).
That is why and this prob will get me banned us over here at time do get kinda pissed off when we are looked on as the little brother as in fact it the other way around really ...we created you guys not vice versa (yes there are other nationalities too ) but in essence when I lived stateside and some said anything I said look I can almost be very certain where you came from ie if you are white (No I'm not being racist in any way) then it pretty certain looking at your features that you are from northern European descent ............I can and I would have a fair bet that Tez could too ....look at city names and say yup that is or comes from us over here or nope that germanic origin or Nordic .........jeez lol even your 1rst president's name ummmm is a town over her lol and I think that is where his ancestry came from
Anyways I'll prob get banned now lol