Play the map, not the leader.
I didn't say Ignore the map.
I gave him positive examples of things he could do, that should he randomly get a leader with this trait.
I've played a game as Hannibal of Carthrage with No Horse, Copper or Iron resourse. I used LBs to attacks my neighbor and capture his iron.
One can do the same with PRO leaders.
One doesn't ignore common sense either.
Let's set up an example.
One starts a game with a PRO leader, AIs starting fairly close with early rush UUs and a high likelyhood to attack (Monty and Shaka, for example), and one's starting Traits are Hunting and Mysticism, like with HRE. So, we will use Charlemange.
Now, it will take AH, TW and to hook up a Horse to be able to build Chariots.
It will take M and BW and to hook up Copper to build Axemen.
It only takes Archery (just 1 tech) to start defending one's cities from an early rush. One can also fogbust with a unit that is more likely to survive barbs, especially on hills or in forest. HRE could then chop out settlers to rapidly expand to a desired location with a defender nearby.
Now, I know you are thinking, he doesn't have any food resourse. One could research fishing or Ag, depending on the map. Now, you are saying but Ag and Archery, that's two techs, I'd rather go for AH. I'd have to say, if the map provides you a wet Corn and a plains Cow, then one could skip the AH and go for A and start the plan as above.
Also, I have archer rushed a close opponent too. They tend to do better than a warrior rush and they will defend a city afterwards better too.
If, I randomally get Churchill of the Vikings with PRO/CHR and starting with Hunting&Fishing and I have mostly seafood resourses and have an early AI with a UU of Swordsman or later, I can rush them with some great Archers and capture their city.
Now, this doesn't happen all of the time, of course. It is a matter of playing the map AND the traits provided, depending on what the situation and your choesn victory condition are for each game.
The comment about not fighting when having an IMP trait, seems like you might be letting the AIs manipulate you into ignoring part of your assets.
Again, it depends on the map and settings. A very fast game speed with an IMP/FIN leader could just tech to redcoats and stomp then. To me, those tech to curissiers to win seem like boring games. Especially, when one can pillage a foe to slow down their research to use earlier units longer on Epic/marathon games to gain more GGs, utilizing the IMP trait to it's full potential.
If I start with DeGaulle, I will likely go for StoneHenge. If I start with Roosevelt, I will likely go for TGL. If I start with Greece, I will likely go for phalanxs. Yes, I play the map too, but I do not ignore my strengths. To start with an AGG leader and Copper in my BFC and not axerush, if the map permits it? That would seem like a wasted opportunity.