Keith - HRC does not require a club to take walk ups, that along with number of dogs per level and number of dogs per handler are all the clubs choice. HRC does limit the max number of dogs per level and the max number of dogs per handler but a club can lower those levels if they want to.
Clubs can also choose to charge additional money for walks ups. Depending on the club/ location / and history of entries walk ups can make or break a club as far as financial forecast. If a club has a history of full flights then closing entries might not be a bad idea. Having done the job of secretary of a hunt the walk ups can be a challenge plus planning for birds, food and workers is equally as challenging.
As for Hunt Sec vs. Entry Express? I don't have a dog in this discussion, I know EE closes a week earlier then HS and if HRC folks are not aware of that they can miss making the entry on line. For small clubs the additional expenses may not be the way to go. Clubs out here have used both.