Yes. The issues around relocating, and would have resulted in much horse trading when Wasps moved to Coventry, is that your new location must not negatively impact on the geography of potential fans visiting nearby clubs. In the case of the move to Coventry, Wasps had to argue that it would not impact on Leicester, Northampton or Worcester. Mainly, this is about non-aligned rugby fans who do, we all know, turn up at games simply to see a game that is on.
The other issue is of academy recruitment and other promotional activity. For example, Wasps agreed that South Warwickshire would remain the recruiting of Worcester, and so on. That is why Wasps retained recruiting links in Oxford.
London is already heavily carved up in both regards, and I cannot see any of the 3 clubs already in place ceding much, and history be damned.
The next issue is the requirement for policing and medical cover. Wherever you set up home, you effectively need the permission of these forces to provide manpower for your games. It wasn't too much of an issue in Coventry. But, when Wasps cast around when looking to move away from High Wycombe, the Met gave a loud and emphatic 'No' to a move back in to London. I cannot think their manning levels have improved, and calls on the force for other weekend activities in the capital have no doubt increased.
I know the Wasps move to Coventry was incredibly rushed, but it was nonetheless complex. It is the reason for the continuity clause in the 'sporting succession' process.