I would suggest that while new hires of H1B might not get paid less, the market dynamics of not having as many alternatives would invariably lead to less valuable retention efforts by the employer. i.e. fewer raises, fewer promotions, smaller bonuses, etc.

As I understand it, H1Bs aren't too bad (transferability is a thing here), but other forms of visas are brutal in this regard.

https://news.ycombinator.com/item?id=13579226 is one example. In addition to the article, HN is in near-unanimous agreement on this issue from the contribution of many H1B visa holders. I've seen it pop up many times.