Lets say in back you have an 11-cog cassette. And in front you have a double. Common choices are the 11-35t, 11-28t, 11-30t, 11-32t, and 11-34t.
With a 50/34 in front, and an 11-25 in back, your lowest gear ratio will be 1.36:1. Highest will be 4.55:1
With a 52/36 in front and an 11-25 in back, your lowest gear ratio will be 1.44:1. Highest will be 4.73:1
With a 53/39 in front and an 11-25 in back, your lowest gear ratio will be 1.56:1. Highest will be 4.82:1
Now lets do the same exercise with an 11-34t in back:
With a 50/34 in front and an 11-34 in back, your lowest gear ratio will be 1:1. Highest will be 4.55:1.
With a 52/36 in front and an 11-34 in back, your lowest gear ratio will be 1.06:1. Highest will be 4.73:1.
With a 53/39 in front an d an 11-34 in back your lowest gear ratio will be 1.15:1. Highest will be 4.82:1.
So why wouldn't everyone want the broadest range of gears possible? Because the spacing between gears in the 11-25 cassette is much closer than in the 11-34 cassette, making it a lot easier on the narrowly-spaced cassette to fine tune your cadence to fall within the best power/cadence balance when riding in less hilly terrain. A broadly spaced cassette will leave you wishing you had a gear between the gear steps when you ride at speed down a long flat or slightly inclined/declined road.
But that 11-25 cassette is going to suck for climbing steep grades. The best cassette for you is the one that provides the low end you need, and the spacing you need. The front end plays into this as well, of course. So the whole thing is a series of trade-offs and optimizations that have to be configured to meet the individual rider's needs given the terrain this rider encounters.
It's unfortunate that triple cranksets have gotten such a bad rap in recent years. Sure, if all you ever tried in the triple-crankset world is low end stuff, it's going to be kind of lousy. Higher end stuff will perform better, but is becoming harder to find. On my Cannondale Synapse, with 105 components I have a 50/39/30 in front, and in back a 10sp 12-30 cassette. With this I get reasonable spacing between gears for good power-band efficiency, while still getting some good low gears (as low as 1:1) for climbing Little Cottonwood and Big Cottonwood canyons near my home. To get this range in a compact double I would need a 34t rear cassette, and in a 10sp setup that's going to leave some big gaps. So I would have to swap out my rear mech including shifters for an 11sp setup to get to an 11-34t cassette, which would still have more gaps than I have in my 10sp 12-30 cassette.
My bike originally came with that 50/39/30 in front, and a 12-25 in back. It was fine living in LA, but not the right cassette for where I ride now that I've moved to the Southeast corner of the Salt Lake valley. I swapped to an 11-28, and later to 12-30, and am not ashamed that the 12-30 is a great cassette for long, steep, sustained climbs.