You have to know where and when to point the laser to a much greater extent than radio and microwaves.
If you want to be noticed, constant illumination is a bad idea, anyway. To maximize the ability of others to detect your signal you should sweep the sky in regular intervals. We know where the stars are, so we might as well target those. With microwaves most of the energy would be wasted into space.
And the receivers must be much more sophisticated technologically (or at least the ways we developed them) for an x-ray laser.
I can pick up the parts to make a radio or microwave alien detector for a few hundred dollars right now. No one has built an x-ray laser digital pickup that I know of. If you want to be heard by as broad an audience as possible you would stick to simple techniques before swapping to more sophisticated gear once the handshank has been made.
Oh sure this is all biased in the human experience but the physical and technical skills to build the different devices are drastically different in absolute terms.
Digital semiconductor detectors for x-rays exist longer than you or me. The first x-ray telescopes were less than 50 years behind the first radio telescopes - compared to galactic timescales that is nothing. If you can reach 100 civilizations instead of one, it wouldn't matter if 2 of those wouldn't have x-ray detectors.
Technological difficulty doesn't matter much. Sure, you could build a microwave detector on your own, but its sensitivity would be quite bad. So it would be very unlikely to detect anything that a more sophisticated system wouldn't. The limit of what would be detected and what wouldn't is set by the state-of-the-art systems and those are constructed by people with the best technical skills.