This is a pretty widely discussed question, and while I think the empirical evidence is so far unclear, there are some obvious theoretical models where costs for large institutional investors (like pension funds) go up. E.g. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2238516.

Pinging (https://www.finra.org/investors/insights/getting-speed-high-...) would be an example such strategy.