Re: velocity and space
But is there any sane reason not to launch at favorable moment only?
They do launch at favorable moments and close fairly rapidly. Note the Dragon cargo flights only have instantaneous launch windows to the ISS - they don't twiddle their thumbs and launch when the ISS is just anywhere.
The shuttle got within 15km of the station in just 3 hours: Quoting David Hammen's reply, "The Space Shuttle rendezvous timeline took 6 hours from start to finish. With 4½ hours to go, the Shuttle was 250,000 feet (76 km) behind the Space Station. With 3 hours to go, the Shuttle was about 50,000 feet (15 km) behind. Relative velocities became slower as the Shuttle closed in on the Station. The last 400 feet were incredibly slow, taking about 40 minutes."
Over a period of 6 hours or two days the approaching vessel makes several burns. This entails making a burn, having controllers on the ground monitor the effects on the vessel's orbit, then making another correcting burn until the errors are small enough for a safe final approach.
Several planned burn opportunities allow you to set up the navigational math in advance: correcting errors in plane, then errors in phase, and final error elimination. A similarity can be seen in shuttle history: It was an achievement in experience and confidence for the US shuttle program to begin "direct insertions."
Early shuttle flights had two planned orbital maneuvering system (OMS) burns to establish a circular orbit. The first (OMS-1) happened shortly after main engine shutdown to eliminate errors in velocity that accumulated in launch and set up an elliptical orbit to the desired apogee. The second, OMS-2, happened 45 minutes after launch (at apogee) to raise the perigee from "Launch Pad 39A" to "desired circular orbit." After several years of shuttle flights and improved navigational techniques, most shuttle flights were able to achieve OMS-1's goals with their main engines, the so-called "direct insertion flight." OMS-1 was finally eliminated, leaving only OMS-2.
Per this mega detailed page, some things are worth noting but they boil down to "rockets are imperfectly precise critters." The shuttles started with two OMS burns to get to the correct orbit and often had manual RCS corrections to the OMS corrections.
The famous precision of NASA's deep space probes in flybys doesn't happen because the probes were aimed correctly at launch. Instead, they depend on correction burns and even continuous correction for things like sunlight pressure. The infamous Mars Climate Orbiter had five correction burns planned and the navigational process was: burn, watch the results, calculate a correction, and repeat. While Lockheed ultimately holds responsibility for MCO's unplanned Martian lithobraking maneuver, NASA navigators watched four consecutive burns leave MCO off course - they saw each burn was not getting the correct results - but decided the optional fifth burn was unnecessary.
Vessels heading to the ISS are dealing with the same thing. The launch isn't going to be quite correct, so that needs to be fixed. Setting up a lower orbit to overtake the ISS isn't going to be quite correct, so that needs to be fixed. Fixing requires monitoring the vessel's flight, computing the correction, and making a burn at a correct time - which may require waiting to perigee or apogee for the most efficient results.
Pardon me for bringing up a game, but the Kerbal Space Program is highly instructive in orbital maneuvering. I'd done everything from manual orbital insertion to manual interplanetary flight and manual landing on another planet and never wanted to use an autopilot mod until I started trying orbital interception and docking. If I was lucky and had an empty weekend day, I could achieve 2 or 3 dockings that left me wrecked. So: MechJeb for that stuff now. A few practice flights and orbital intercept attempts might help make these answers more visceral for you.