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I know that head tube angle affect steering, but does seat tube angle affect maneuvering somehow? As long as I compare a few models, they are between 72 and 74 degrees, and greater the frame smaller seat tube angle. So I guess difference by a few degrees doesn't have considerable effect.
Here're the comparisons.
As for sheer maneuverability, seat tube angle may in some (rather extreme) cases affect wheelbase, which affects stability at variety of speeds. Also seat tube angle will have some minor effect on the position of rider's centre of gravity making it slightly easier to descend with smaller seat tube angle... I guess it would be an unnoticeable difference though.
But main aim of angled seat tube is above all to make pedalling more correct in a biomechanical way, thus more efficient..... and making it possible for a rider to reach the ground while still being on the saddle, say when they're stopping. For the right distribution of stresses within your joints you need an angle adjusted to your body - people with longer thighs will need smaller angle. In general too low angle encourages lower cadence and more forceful pedalling which isn't very good for your joints. What's interesting is that it doesn't work the other way round - it's possible to ride relatively safely with very high angles - it's usually 78-80 degrees for TT bikes. (I meant to put an article titled "Myth of K.O.P.S" for Sheldon Brown website, but the link doesn't seem to work)
Here is the link to Sheldon's Myth of K. O. P. S. (knee over pedal spindle) article.
Seat tube angle can be quite well made up for with fore-aft saddle position, so 2 degrees in difference can be easily neutralised. And the differences in angles between sizes may come from various sources:
Or it could be a mix of the above, we should ask the designers.
It impacts weight distribution which in turn can impact handling. It also impacts front center. Bike geometry is more complicated than people think. I hear people all the time say a frame with a 57cm top tube will have more reach than a frame with a 56cm top tube. This isn't necessarily true because of the seat tube angle. Team mechanics usually rely on a form similar to this one: https://s3.amazonaws.com/USACWeb/forms/mechanics/RoadPositionChart.pdf
When a team switches bike manufacturers or a rider needs a new bike built up we'll pull out this sheet and use it to assemble the bike. The most important numbers are the distance form the center of the BB axle to the top of the center of the saddle and also the horizontal distance from the tip of the saddle to a line drawn straight up though the center of the BB axle. These two numbers determine where your butt is in relation to the pedals.
The next most important numbers are saddle to bar reach and horizontal drop from saddle to bars. The chart above shows saddle to bar distance being measured to the stem clamp but most pro mechanics I've seen prefer to measure to brake hoods to account for differences in forward reach from one bar to another (important if switch bar brands)
The important thing is to figure out the position the rider needs to be in and adapt the bike to that and not the other way around.
Even if you're not a pro racer it's handy to have one of these forms filled out. It's surprising how even a minor change can have a major impact. I've known more than a few riders who developed knee pain after switching shoes or pedals. Turned out the new shoes/pedals were a few mm thinner/thicker than the old models and they failed to adjust their saddle height accordingly resulting in strain on the knees.
