This would basically make the tournament blind pick, but the benefits could be very fun, building ships which can cope in various maps and against multiple opponent loadouts, which chances are means less meta and more disable (control) or reactive (mix of kill and disable) builds and play styles.
Given, teams could conspire with each other because they would be able to see who their next teammate would be. I'm not saying people would, but it would be quite easy to.
Perhaps the table/scoreboard should be released after the team's next ship selections... but that's a short amount of time, and not all team leaders may respond with next week/round's ship. Plus, figuring out the scores wouldn't be that difficult, it would just be time consuming. A solution is giving the table itself a degree of randomness in picking teammates.
Substitutions are something that comes up a lot.
Something I've seen work in other tournaments is this (language adapted for GOIO):
Each ship/team will have an unlimited roster. Anyone currently in that roster may play on that team's ship. Anyone on a different roster may not join that ship, even if they are of the same clan. A player not in any roster may play for any team at any time, however, must be added to the roster after doing so. The Ref should take a screenshot of players in the server at the beginning of a match in order to determine who is on a roster and who isn't. After a match starts, no subs are allowed mid game, even in the case of disconnect.
Teams will have unlimited "adds" for two weeks. After that, they may add 2 people to their roster per week. Teams always have unlimited removals. A team captain or the player themselves may ask for removal.