The diplomacy hit for capturing an enemy city is the same whether they backstab you or not. DoFing with a civ who decides to be a jerk and get denounced by everyone will drag you down and get you embargoed in the world congress and all your luxes banned.
You have NOTHING to lose by abstaining from DoF and everything to gain.
P.S. having to spam military units to fend of invasions because you got to close to a spazzed out civ will impact your science/gold/production.
Who says you need to take cities? That's nowhere in the mix here, and not what we're talking about.
Why are you choosing poor friends? I didn't say accept every DoF, I said look at the diplomacy and be in the "popular" group.
Why are you getting anything passed against you in the world congress? Your friends will vote no. You control city states, right? They vote no too. I've never been embargoed, not once. Occasionally a lux will slip thru, but only because I'm pushing my ideology or religion thru and I can't spare the votes.
I'm telling you that what you are proposing is fine when you do not understand the mechanics of diplomacy, but as soon as you figure them out, it is a poor decision to be the lone wolf.