It’s responsible for all the mass of *fundamental* particles.. fundamental particles can’t have explicit mass terms because of gauge invariance
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It's the opposite of a problem! that's why gauge theories are said to be maximally predictive, the more constrained we are the better The higgs transforms under the chiral symmetry group (like left handed fermions).. this way we can write down gauge invariant interactions.. 1/2
whereas the mass term doesn't transform under the symmetry group, and so you'd pick up an extra phase if you try to transform something like q_L q_R (and so it's not invariant) ..
