Put some blinkers on for a minute and block out these Enablers 
You might end up with 2 or even 3 very Judgey adult cats .
You'd have to keep the kittens indoors , wait until you can get them neutered and vaccinated ..whenever that might be .
If you get male kittens and they start to spray , you might not be able to neuter them early enough to stop this becoming an ingrained (very smelly) habit .
Why has this near neighbour allowed her female to breed? Is it an accidental litter ?
I can 100% see the appeal , especially if it means these tiny meeping kittens are going from home-to-new home and by-passing being shunted about . But , your Resident Cats might not get along.
I have resisted any new cats , my pair are established and happy and the applecart does not want to be upset .
I'm sure I could get a new one (fairly easily ) I've had a Homecheck when I got them and a follow up visit in December . But I'm sure my cats would put in a bad word about me 
(DH was all you got five guinea-pigs and they didn't get on . Yes but they were in 2 groups , a 3+2 , and I could manage them. Cats are completely different )
And yes , they are ££ .
It's a lovely thought but Head not Heart . 