The time between Auto Attacks is not based on server time, it is based on weapon. Every weapon has a stat called 'delay' and this is the time, in seconds, between auto attacks. You can test this out yourself by timing the time between Auto Attacks. I did do this myself, timing over 5 Auto Attacks between Monk (2.56), Red Mage (3.44) and Paladin (2.24). I only done one test each, but it was enough to show the difference with the Monk taking ~10:30 seconds, Paladin taking ~11:30 seconds and Red Mage taking ~17:30 seconds. Note that Monk takes less time because of Greased Lightning, but if you were to calculate that out, it would have taken them ~12.80 seconds, which, when divided down gets close to 2.56 seconds.
As a small detail, you will notice that weapons for the same job will always have the same Auto Attack delay, this wasn't always the case and if you look at older weapons, you will notice they will have different delays. However, they were always balanced so that the auto attacks would always provide the same damage (assuming same ilevel). As an example, Paladin's Giantsgall Longsword and Mail Breaker have stats of 42.40 AA and 2.4 delay and 38.16 AA and 2.16 delay, if you divide the AA by delay, you get ~17.6 for both, so they both do the same total damage over time.
As a reference, with stats scaling as they currently do, if you had a theoretical set of gear that had maximum tenacity, you reduce all damage by ~12%. (As a reference to where I got that number from: https://youtu.be/stgUbtFKu74?si=TzRF0yS78uio6vka&t=93 also goes over why it is considered bad).
Now, as for tanks taking more damage, you have to remember this is something that will affect both tanks and healers. If the tank takes more damage, they healer has to heal more. If you stack tenacity, it would seem an obvious conclusion that the healer would have to heal less, but this isn't necessarily the case. I'm just going to go straight to the heart of the matter and that is going to be, will stacking tenacity save the healer a GCD heal? If the answer is no, then there is no point stacking it, if you can, then that means there is a break point for that to happen, so people will just stack to that value and ignore it after that, effectively making it a new accuracy stat. This will also mean SE will always have to make sure you can have the desired amount of tenacity, which was a nightmare in HW trying to get and keep enough accuracy even whilst upgrading gear.
Ultimately, forcing players to have a certain stat spread because the game forced you into it isn't fun, you should be able to gear as you want, which amounts to crit > all, but that is a different discussion.