Why use Levenne's Test for variance difference testing?

[c-hoffmann]

In writR, variance testing is done with Levenne's Test. However, as far as I understand, Levenne's Test is more prone to type-II-error, which means it more often does not detect an actual difference in variances. Why not use F-Test or Bartlett? I'd rather use a corrective method too often (since Levenne's Test has a lower Type-I-error) than not correct for an actual difference in variances - or am I missing something?