That's not true, there are plenty of side-channel attacks that fall squarely within the realm of block cipher cryptanalysis. Examples include Differential Fault Analysis (DFA), Correlation Power Analysis (CPA) and more.
It's true that practical side-channel leaks on software block cipher implementations tend to be microarchitectural (e.g. cache timing), but that's only because the "easier" attacks are already mitigated or considered out of scope (e.g. no physical access).
It's true that practical side-channel leaks on software block cipher implementations tend to be microarchitectural (e.g. cache timing), but that's only because the "easier" attacks are already mitigated or considered out of scope (e.g. no physical access).