Here's my take on trade offers.
In my experience from GC3, the offer tends to be for a bunch of stuff including a hefty sum of credits on my side of the table, and a few things on the AI's side of the table, which I may or may not need. There wasn't any way to look up what a resource could be used for e.g. Epimetheus Pollen is used to promote administrators to ministers, so having a stockpile of it is very useful if you're an expansionist or you like building a lot of hypergates.*
* I've only just started using hypergates in GC3 and one of my annoyances with them is that when a hyperlane goes through an obstacle, ships will path around the obstacle but in doing so, come off the hyperlane for a bit before going back on. So, I build extra hypergates to adjust the hyperlane onto a clear path.
In addition the AI didn't seem to stockpile or do missions to get a variety of resources like the human player. That's even though they were pretty good at making an impressive collection of colonies. So, there wasn't a lot of reason for me to trade. If I really wanted to buy a particular resource, then Intrigue expansion offered a way of doing that without negotiating with other empires.
Rather than having a cooldown of a certain number of turns on trade offers, the AI should think about whether their trading needs are unsatisfied when deciding to contact a player. Instead of opening up a trade offer every time, maybe they can just say what they are particularly looking for, and then let the player decide whether to open the offer window right at that moment. Maybe the player can hook up a resource to a starbase and/or ramp up production of that resource and thirty turns later have a decent amount to trade.
And also, having a nice sum of credits to trade for that is a plus point in the AI's favour.*
* The AI in GC3 seemed to have difficulty with their finances. The surveillance panel in the espionage screen showed that some of the factions would get down to just a handful of credits, at which point they would ask me for a handout.
The AI would also look to buy strategic resources like antimatter, which I was be reluctant to part with, because antimatter was used to add some missile weapons to ships.
Hope this is a useful perspective.