a nest is an item required to raise a brood of nestlings- to provide safety and shelter. Once the nesting season is over then it has fulfilled its function and has no further use. An adult bird has no need to 'live in a house' as we humans do. Any sheltered perch will do for sleeping on. The one exception is that during cold weather small birds will use old nests for roosting- often large numbers will huddle together for warmth. If I remember rightly wrens hold the uk record for that- over 20 were counted leaving one nest during particularly cold weather. A
And no- blue tits are NOT particularly territorial. Outside the nesting season they are generally found in small flocks.