Showing levels wasn't just a way of letting more experienced players recognize player competence, but it was also a way to help new players judge the level of their enemies so that they could decide whether they wanted to go against them or not. I used to tell new players to watch out for player levels and choose matches based on that. As a level one captain you might want to reconsider going against two level 30 ones and you might want to find another lobby with people around your level. (Please do not tell me that levels show no relation to player experience or competence, in most cases it is quite easy to guess match outcomes based on just that single aspect.)
With level visibility partially gone, experienced players can still easily judge the situation (you can click on names or just check out ship loadouts, look at crew setups, familiar names, let's be honest, this is a small community, we know each other etc), but new players are at a disadvantage because they cannot even rely on level indicators anymore. Also, I am not quite convinced that one's hidden match rating is a valid indicator of one's actual in-game performance, so you can never be entirely sure that the people you were placed against by the matchmaker system will really be at your level and competence. Even if there was no human involvement in lobby setups, the glicko system could overlook certain aspects of the gameplay.
Just to give an example, I often like to join suicide sides for fun, eg ships that the captains have abandoned in ongoing matches or ships with three powder monkeys on it. Even if realize that I am on a losing side, I often stay through the match, especially if I had fun with some players on the ship. Because of that I have a lot of lost games, and I guess my rating is quite low (in fact I noticed that I keep getting placed by matchmaker into lobbies with level 10 people around hehehe). Yet, if I am placed into a good crew on a strong side, I can be as competent as many other players whose rating must be much higher than mine. The rating system will mark me as a weaker member, and will consider the match "balanced", but we will still most likely win the round. Wouldn't my actual player level be more accurate in this case?
Also, what is the point of hiding levels before a match starts, and revealing them during the match (tabbing) or after it? It feels like a bad surprise for low levels (BEFORE MATCH: "Hey guys, don't worry, we should be fine, it's gonna be fun" DURING MATCH: "Dang it, look at all those high levels on the other side!!")