My boss says we don't need any engineering managers. Is he right?

This seems like the direction lots of companies are taking. Engineer roles are expanded more and more. From a certain perspective I see that because engineers have the expertise they can better organize and communicate development milestones, coordinate between designers and product owners, and test the product before also rolling it out (not to mention telemetry). So adding on top of this a little more management is probably not a huge change, that said it doesn't come for free, and I'm not sure companies that move in this direction are aware of what the trade-off really is.

It would be like taking a soccer/football team and having all players expand their roles such that every player has to be a goalie, a defense, and an offense player that scores goals. When everybody has all the roles, it may work out but it is not as efficient as the assigned roles with clear boundaries that create the best teams. From this angle it is very important to have the different roles in the team, and for each person to optimize their role and learn to work smoothly with others.