I'm okay if they decide to limit people from trying sites in beta because other popular gambling sites like Luckybit only choose a few people before opening it to the public. Besides, we can still try the beta version by following the giveaway in the Stake forum.
There is no guarantees that Stake will get better idea if they open the beta stage of the sportsbook publicly. Other many sites did not even conduct beta stage before they launched officially so beta stage wont bring significant differences whether it is opened publicly or privately to some users only. In case of heavy load, do you think that sportbook will get heavier load than other common games such as dice or crash? Even if there will be many players opening the sportsbook game at the same time, I believe Stake is well experienced enough to manage it. At least it has been proven with their other games, so you do not need to be so worry about it.