The reason that is looks extremely awful on Edmure's part is that the series completely messed up that part. What happened in the books is much better to understand. That's why even though you don't have the asoiaf tag, I'll quote the books.
Like in the show, Freys had Edmure on the gallows each day from dawn till dusk.
That part is the same, and Jaime first made sure Freys stop acting like it.
Blackfish could resist to the siege.
This part is different. Due to its location, Riverrun is easy to defend. And in fact, Blackfish did not get it from the Freys, he was already there so he had plenty of time to obtain provisions for a long siege, approximately for two years. With winter approaching, he had a chance of holding the fort.
Jaime threatened Edmure to yield the castle.
"I will assault the castle tomorrow. First I will send the riverlords. You will first be killing your brothers you fought together."
Except Lord Blackwood who did not surrender and except Lord Bracken who were besieging Lord Blackwood all riverlords were there in the siege.
"Then I will send the Freys. I have no shortage of them."
Frey army was largely intact. They withdrew after Crag has fallen.
"Only after the last Frey is dead, you'll be fighting against Lannisters."
I think he brought an army around 4000. Soldiers from the Westerlands constituted roughly half of the army.
So, Edmure realized how impossible the situation is. Jaime offered him an exile in
Lannisport Casterly Rock, not a dungeon cell in the Crossing. He went in there to negotiate a truce with the Blackfish. But he did not attempt to capture Blackfish.
When Jaime asked where the Blackfish is, Edmure did not respond. After Jaime threatened him with a cell in
Lannisport Casterly Rock, he responded "Fish can swim, we opened a gate in the water and he swim through it."
So, as you can see, neither Edmure is a broken idiot nor Blackfish is a romantic fool.