The disadvantage is that its measures aren't very consistent across hues.
Pure sRGB blue, #0000ff, has an HSL lightness of 50%. So does sRGB yellow, #ffff00. But the blue is objectively a much darker colour than the yellow (try text in each of those colours against a pure black background and see which is easier to read).
Similarly, sRGB magenta (#ff00ff) is significantly more saturated/"colourful" than sRGB cyan (#00ffff), despite each having an HSL saturation of 100%.
And hues are not evenly/perceptually spaced around the colour wheel: the angular difference between chartreuse (HSL hue 90°) and spring green (150°) -- which are distinct, but both obviously shades of green -- is the same as that between rose (330°) and orange (30°), which are very different colours.
None of this is to say don't use HSL. There are other, more perceptually consistent colour models, but they have their own problems: as well as having mathematically more complex transformations from and to sRGB, they tend either to have irregularly shaped colour spaces (so the colour wheel becomes the colour weird-bumpy-thing, which changes shape and size at different lightness levels), or to make compromises that introduce some of the same problems as HSL, or even cut out some sRGB colours entirely.
We just need to be aware of HSL's limitations, and use it with care.
You can do things as vary hue by a few degrees, vary the saturation or lightness by fixed amounts, use opposite hues on the color wheel, etc. Some useful tricks to have if you are doing color grading as well. There are all sorts of known useful ways to combine colors.
The key insight here is that what is pleasing has some heuristics behind them. It's simple math once you figure that out. For color blind people, color contrast works differently for certain hues.