Isn't that the whole point of relocation though? Keeping the same team colours, jersey etc, just playing in a different location. Surely re-branding with a completely new identity is just the same as killing off one team and replacing it with another.
No not at all...
The point of relocation is to relocate the club (i.e. the business side of the team) and along with it the license to another market, whether or not the team re-brands or not has nothing to do with it.
Many of the most successful relocated clubs re-branded, the Houston Oilers became the Tennessee Titans, the original Cleveland Browns became the Baltimore Ravens, Charlotte Hornets - New Orleans Pelicans, etc, etc.
To be honest the ones that re-brand are successful more often then not and it probably has a lot to do with them re-branding, it probably stops the team from trying to have a finger in each pie (which outside of very specific cases never works) and forces them to fully commit to the new market.
Take North Sydney for example. Do you think if given the option of relocation, merging (which they did and failed) or being dropped from the competition altogether (which of course happened), what would they have chosen?
A lot of It depends on the details of each situation. For example if a merger that was completely in favour of the Bears (to the point of effectively being a hostile takeover like the Dragons "merger" with the Steelers) or relocating to Timbuktu were on the table then I think most would go for the prior over the later.
But as an ex/sort of still am Bears fan (it's complicated), and with hindsight now that the emotions of the situation have cooled, I would have preferred pretty much exactly what has happened over all of those options: Continue to exist as the North Sydney Bears but play in a lower tier competition, the only thing I would have done differently is seek a broadcaster willing to broadcast the teams matches, apart from that I think it's the best outcome (or it would be if it was handled properly).