At least regarding gmod hide and seek, I don't know if that would be a good idea. Under the presupposition that we did so and our HNS server got massive support and people started playing games on hns, they would flood the server making it difficult again for admins to get on. For this to be even tenable we would have to increase the player slots to probably at least 64, but then the problems becomes lag from the sheer amount of people engaged with the server at once.
There is also the potential for multiple gfl hide and seek servers, where the problem there will be that one server will definitely be more active than another, and then people are really just going to wait to get on the most active server and create different problems.
Regarding competition, I don't really understand how it would work regarding hide and seek. Would it be that the winner is the person who gets the most points on a specific map, and if so what is the actual prize? Also, even if that is how it worked, I don't see it really getting any real traction. It's hide and seek, and the competition would really be artificially injected. It's true that we have try hards on the server, where I sometimes have fun putting the effort in.
Although, there may be a way that hide and seek could work in a competitive sense that might actually be very interesting. For instance, let's say that there is a separate locked server, and 32 people would be included if they signed up for a specific tournament time(if they don't make it on time they forfeit automatically, though there can be some leniency)(there should also be some requirements to join the tournament, such as a certain amount of time playing with gfl hns, and a relatively clean warn template). 1 person is the designated starting seeker(it'd have to be situated so admins can force choose the starting seeker), and that person(preferably a skilled admin) has the goal of tagging everyone. If everyone is tagged in 5 consecutive rounds(the duration of a map), then the starting seeker wins. However, if everyone isn't tagged in 5 consecutive rounds, and we have a set amount of hiders in some round, then all of the tagged people would be kicked, with all that being left is the starting seeker and the hiders that survived. However, after a certain threshold of people being removed for getting tagged and losing, the map is a changed to a smaller designated map so it becomes more difficult to get away with surviving the round. For example, a large map like Geekroom or littletown from 32 players to 20, and then might turn into something like museum from 19 to 10 players, and then lower to smallotown or plaza from 9 to 2 hiders left. If there is 1 hider left in the end, then there will be 1 more round between the seeker and the hider. If the hider is tagged, the seekers wins. if the hider survives, the hider wins. The reward could be a large amount of pointshop points, and maybe a special pointshop item limited only to tournament winners like that.
This would probably be very fun, and tournaments could be done semi monthly. They could be hosted on something like twitch if someone wants.