That was a defensive campaign and a punitive/securing the border expedition, the intent never was to conquer that part of Germania
Even, putting aside the already noted M. Aurelius' intentions, him planning to and taking the war to the enemy territory, either to retaliate by their earlier invasion or as way to destroy them and preempt any possible future invasion... It only could be constructed as an offensive campaign.
What advantage do the Romans get from this? IMO they wouldn't be that interested in Britannia
Besides from as was noted upthread of Rome possible interest for recruitment of foreign warriors either individually or even as whole groups, as auxilia (like IIRC Constantine, fielded in Milvian Br battle). Britain, still would be of interest for Rome as trading partner and for secure the undisturbed flow of the British mineral resources. Also, to put attention on the closer Barbarians and to exert influence either directly or indirectly through trade and playing some chieftains against others or mediating between them, was kind of of standard policy for most of the empires (with competent enough rulers/bureaucracies) through the History.
A conquest of Germania isn't that difficult, before the Battle of Teutoburg the area was pacified and could be compared to Gaul after Caesar, if the campaigns in Germania continue then the Romans will need only a decade or two to manage to pacify the area, they didn't do OTL because Tiberius was worried about the growing popularity of Germanicus and because doing so would be extremely costly.
Should be noted that while Romans losses equivalents to the Teutoburg ambush ones, while if not common, neither they were unheard in Rome military history/military campaigns. And that both Rome lack of political will and the necessary continuity on it as for prioritize it enough as for let be involved in a such multi decades effort. But, particularly Tiberius' actions and political-military decisions could be attributed, mainly that he wasn't a military leader/able general and looked for an 'easier' target on Britain and also, as you noted, to internal political reasons/court intrigues.
But, it, in fact, started way earlier and his decisions/actions was shaped by the at the times ongoing and far more concerning (in terms of scale and deployed armies), for Rome, the Bellum Batonianum/Great Illyrian Revolt.
It wouldn't last very long
Perhaps, but aside that it wasn't in discussion, it would last long enough as for that it would provide both advanced defense and if necessary for it be a base for the next emperors military expeditions.
Also means there will already be Brit's in various places who will send for their family's when Rome enters terminal decline. Same result as the Goth's had OTL...
It would show its effects way earlier with those even if no more than few tens or hundreds of surviving veterans back in Britain. Would be used to an monetary economy, after to have been deployed/fighting through the whole empire and probably well off in comparison to most of their neighbours/fellow tribesmen. It would probably, these Britons would brought with them new ideas/religious beliefs and ways to think/perspectives from the ones commons back in their tribal homes. Would be probably to cause changes and/or along with trade with the Empire, to stimulate the island, even if primarily at local /regional level.