A diamond 1 player is way different than a diamond 5 player in terms of skill level. If two people say, "Oh, I'm in diamond" then you can't tell if there's a major skill difference without knowing more specifics. The title change alone can add clarification.
Also, the fact that it's insulting is temporary. The climb is a lot shorter for lower ranks. For example, take the two lowest. You think that it's going to be distributed like this:
Silver 3 | Bronze 1
Silver 4 | Bronze 2
Silver 5 | Bronze 3
Bronze 1 | Bronze 4
Bronze 2 | Iron 1
Bronze 3 | Iron 2
Bronze 4 | Iron 3
Bronze 5 | Iron 4
but it's going to be distributed like this:
Silver 4 | Bronze 1
Silver 5 | Bronze 2
Bronze 1 | Bronze 3
Bronze 2-high 3 | Bronze 4
Bronze low 3 - 4 | Iron 1
Bronze 4 | Iron 2
Bronze 5 | Iron 3
Bronze 5 | Iron 4
Because of the amount of players that are in bronze and silver as compared to higher tiers, many people feel hardstuck bronze 5-3 for example. With this new system, you would climb from Iron 4 to Bronze 4, making them feel as if they've scaled a tier. This strongly improves the player mindset psychologically rather than deal with the continuous frustration of feeling stuck after a couple matches. The other thing is that now that Silver 4 is Bronze 1 in this scenario, Silver 1-3 will be redistributed within Silver 1-4 due to a high concentration of players in that tier. All in all, redistribution based on number of hardstuck players improves mindset in lower tiers, and more accurately titles different skill levels in upper tiers. The example I gave is not necessarily exact, as riot has probably spent a number of months looking up stats and testing the best way to boost the effect of the change but hopefully you understand better that the change is not the same as 5 tiers x 5 divisions + 2 tiers becoming 6 tiers x 4 divisions + 3 tiers.