It would be silly to use the X-37 as an anti-sat weapon: it's too expensive. Think of how cheaply SpaceX is putting up Starlink! A single Falcon 9 could probably put up a bunch (20? 30?) of antisat weapons that only ever raise or lower their orbits and fire .22s at their targets. The idea is to disable targets with as little debris as possible.
With larger anti-sat sats you could actually latch on to the target and de-orbit it for zero orbital debris destruction. This requires many more, much larger such devices because while it takes relatively little delta-v to raise or lower an orbit, it takes a lot more to match an arbitrary target's orbit (to which more fuel has to be added for de-orbiting).
> antisat weapons that only ever raise or lower their orbits and fire .22s at their targets.
raising your orbit is the hard and expensive part, it takes a lot of propellant, which generally rules out smaller vehicles, right?
And if you want to destroy a satellite, you need a lot of kinetic energy, which for a tiny projectile means lots of speed relative to the target... But since your absolute speed determines the height of your orbit, the only way to get more than ~1000 ft/s is to have your gun-sat in an opposite-direction orbit to the target, right? And isn't it the case that our satellites are all orbiting in more or less the same direction, since they launch from canaveral and have to head east to be over water?
You don't really need a lot of kinetic energy, it's not like satellites are armored. I'd think a pretty small kinetic energy, like a rifle bullet, would do it (depending on where it hit, obviously.) The trick is delivering that small kinetic energy...
The only issue is that using kinetic weapons greatly increases the risk of Kessler Syndrome; in other words premature mutually assured destruction. Kinetic space weapons are so easy to get wrong with outsized repercussions.
Otherwise raising orbit is expensive(ish) depending on whether you want a circular orbit. Matching an orbit can be expensive. If the target has auto avoidance like Starlink does then matching orbit becomes war of attrition; even getting the target to burn off its fuel is a win as it will drastically shorten its life span.
Deorbiting is relatively easy at LEO, just increasing frontal area is a cheap way to achieve it. Above LEO would normally require fuel of some amount.
Changing the altitude is fine, with all the electric propulsion that is available nowadays. You just need enough power and that means big deployables. The main issue is orbital plane changes, meaning that in the future, satellite-to-satellite weapons will not rendez-vous with the target but just do a quick approach while being on a different orbit and send/drop a low speed projectile to collide with the target. All this is already possible on a 100kg-class satellite.
Can you identify a time when cost was obviously a signifcant factor in a military choice? To me it seems that cost is low in the grand scheme of things.
If they could have 1,000 asat sats, they'd want to have 1,000. Can you imagine them saying "sure, let's just have an X-37B, one, just one, it will do"? If you need these in a shooting war, 1 ain't gonna be enough. You need lots of them. You can't have lots of them if: they're big and heavy (launches are too infrequent and too expensive) or if they're too expensive (you want 1,000 but can only afford 10).
With larger anti-sat sats you could actually latch on to the target and de-orbit it for zero orbital debris destruction. This requires many more, much larger such devices because while it takes relatively little delta-v to raise or lower an orbit, it takes a lot more to match an arbitrary target's orbit (to which more fuel has to be added for de-orbiting).