It was quite rich enough for the Angles,Saxons and Jutes to raid and settle and for Rome to try to hang on to it for 400 years
Saxons, Angles and Jutes settled there mostly because they didn't had much choice : they didn't have the possibility to takeover more populated territories or richer.
The Frankish peoples, thanks to a continued alliance with Rome, enjoyed not only a more strong organisation, re-using many roman features even before their entiere conquest of Gaul knowing that Frankish settlers were present in Belgica since the III century).
The difference between Saxony (by Christian charity, let's not talk about continental Angles and Juteland of Migration Period) and other, more important, migrating people in all regards (especially numbers, military power and organisation) is to be understood.
Britain was...an opportunistic choice, let's say : of course Saxons and other western Germans that migrated on its shores was still richer than their homelands while being ravaged at the end of V/VI by plague, low population (2 millions in VII, maybe. To compare with the 7 in Gaul, both being "maximalist" guesstimates).
Now, for Goths, the question is clear : why bother going North, and settle in the roman equivalent of Coventry (yes, Roman Coventry is Coventry. Stay focused) when you can takeover closer, richer provinces as Gaul, Hispania or even Africa?
At the very best, you'll have a Gothic king launching such a campaign and all the others saying "Okay, you do that".
I didn't say that they would try to keep holding on to it. It was when the Situation over the Rhine got so bad that the Romans abandoned Britannia.
It's one of the factors : Britannia was tought of being left quite many times before, not only because it was costly, less interesting to defend than...say anything else in West, too open to invasions, raids and rebellions. It doesn't mean Britain wasn't interesting for raiders, but a withdraw of troops for saving more precious lands makes more sense than investments, in a short-range focus.
They had fought to keep it before when logistically all they really needed was some Naval Bases on the Channel coast.
Britannia was already quite damaged by Saxon and Frankish piracy since the IV century, honestly (without talking of plague) and troops were taken to continent before 407, this date being more symbolical as the very last ones were took. Since the end of IV, really, most of the troops were used elsewere.
The Empire could no longer afford such medium-term strategy : they needed troop, less for reinforce Rhine border, than have a military presence on the hinterland (Was one of the roman weaknesses : once crossed the border, there was few troops able to withstand a raid).
Plus as hinted in Cato's Cavalry if several idiotic Roman Generals hadn't tried for the purple Britannia could well have held its own even in something approximating OTL.
I really think it wouldn't have worked : the situation in Roman Empire made the armies the arbitraries of Empire. Would have generals in Brittania (that probably didn't much felt tied with the province, and far more with theire troops) refusing to take the purple, their troops would have probably chosen another leader that would have.