I can only answer for the FS I'm in that has restrictive trading rules. I am not the AM there, but one of the reasons I joined was their 'no cross trades' rule.
I prefer to build my city and run my trading around balanced goods within tiers. Since the game demands overall on Tier 1 goods is higher than that of Tier 3 goods that means I build fewer T3 factories and trade fewer T3 goods. That's much harder to do with cross trades, so I stick to same tier trades. While my first city is in an FS that allows cross trades, I looked for one for my 2nd city that did not. I wanted to see what it was like to play with players who used my same approach.
Since that FS has been around for forever, there's been a tradition of large cities sweeping the trader of all FS trades daily. There was never an issue with trades being taken. As I've grown there, it's definitely easier to take trades if you sort for 'FS only' and are guaranteed all trades will be 2* same tier trades. Many times, you can just click on them all without checking anything and remain fairly balanced regardless of your boosts.
It's fine in my other city (where I am AM) that allows cross trades, but I expect to work harder in that city anyway lol!
The 2nd one was built after a year of playing the 1st one, so I made fewer newbie errors and designed it to be a place I can pop in easily and just play. It's a Gold Spire and 13chest/week FS, so it's not like there's nothing to do over there, lol! I just don't have to balance out my unbalanced within tier goods while I'm there. It's more time to devote to the things I find fun in the game.