It's an established phenomena. But, just because it's established as a concept, doesn't mean it's prevalent, or especially not that it could be used to explain simultaneous increases in prices across the entire economy.

Here's an introductory article on price leadership:

https://www.investopedia.com/terms/p/price-leadership.asp

Breaks it down into "barometric", "collusive" and "dominant" categories. Going through each one -

Barometric being the phenomena where all the firms in a space look to the dominant firm for indication on what to do with their prices. Assumes heavy market concentration in the dominant firm and a marked imbalance to analyze market trends or predict upcoming cost shifts on the part of other companies. Does not make any sense in a space with several near-equally sized entrants in the market exist with similar capabilities for determining prices and macro conditions.

Collusive being where they have actually agreed to fix prices together. This is of course illegal and requires ongoing coordination across basically every major company in the economy. This is mostly what we've been talking about in this thread and requires extraordinary proof, because the level of coordination required to make this happen is extreme, especially across not just one industry, but every industry. Or, to be fair, at least the basic industrial/manufacturing industries upon which all other industries depend.

Finally there's the "dominant" category. That's where a single dominant firm (or cartel of multiple firms) is setting prices - particularly, setting them downwards - and other smaller firms are forced to lower their prices to survive. This doesn't make a whole lot of sense with upwards price-fixing, because less dominant firms become more competitive as a result, not less.