Quotes by MBB:
"1) is it really going to make a big difference,"
Yes.
"2) if so, would it be a good idea to convert all of my bikes to these systems?"
Yes. At least your road bikes. Well, maybe leave a short hop commuter with flat pedals in order to be able to wear street shoes and walk around at your destination.
"My last experience with anything remotely like this was with cage-style systems 20 plus years ago, and I hated that."
Why did you hate toe clips? Did you use them with or without cleats?
I was a late adopter of clipless pedals...waiting until Campagnolo manufacture the remarkable SGR pedal/cleat system in 1988.
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As much as I loved toe clips and straps with deep slotted cleats, the clipless pedals were much more comfortable, easier to get into (Campy had a ratchet mechanism built into the pedal axle that held the pedal in whatever entry position you preferred until you clipped in and disengaged the ratchet, allowing the pedal to then spin freely) and easier to get out of (adjustable release tension, no reaching down with a hand to release the toe clip strap).
The modern pedals from shimaNO, Campy, Look (they manufacture Campy's pedals in France), Time and the rest are the cat's ass for sport-level to racing road cycling.
Don't bolt your first pair to that new Tarmac! Try a set on one of your older, less expensive road bikes to get the hang of it. They do manufacture 'beginner's' clipless pedals that are even easier to get into and have a lower release tension to facilitate fast, almost effortless unclipping.
You STILL have to remember to unclip, but that becomes automatic after a couple of hours on them.