Sorry for the long post. I will argue where and why the current Premade Group Finder is not optimal, and suggest some improvements. This is not meant to be about wetter there should be any group facilitation tools or not. There are already plenty of threads showing opinions vary on that subject.
The Premade Group Finder (PGF) tool was introduced to help people firm groups for running ingame content. Alternatives exist(ed), oQueue, OpenRaid, but an ingame Blizzard utility made this it far more mainstream. Going by participation, the tool has been very successful.
Blizzard has other group creation facilities in the game, namely Raid Finder (LFR) and Dugeon Finder (DF). These reach an even wider audience. The most significant differences between these latter 'finders' and the PGF is that for the player looking for a group to do a dungeon or LFR raid, they allow the player to 'click a button', and continue playing waiting for an eventual queue to pop, and that the player is 'transported' to the content. Matchmaking is purely algorithmic, a group leader is determined by the machine, but that leader has no a-priory influence over group constitution and composition. In contrast to that, in PGF the self appointed raid leader can set minimal requirements and have control over how (s)he composes the group based on limited information (in practice ilvl, maybe some achievements, and role).
Many people have argued that this control by the raid leader is needed to ensure a reasonable success with more challenging content (although i personally believe machine learning techniques have been shown to succeed at prediction/composition tasks far more complex than this). For people willing to organize groups (a tiny percentage of players), the system works very well. However, for a significant group of players, the PGF tool is a frustrating experience consisting mostly of a long period of active application and rejection, symptoms of which are for example the 'only groups asking for irrational ilvl requirements that far exceed the ilvl dropped by the content' complaints voiced on forums. I guess even the most ardent achiever can understand being submitted to hours of rejection is not a 'fun' experience for what should be a reasonable application (running content that still has a chance to drop an upgrade).
Where does this situation come from. Simply put, it is a self-reinforcing system. People willing to start groups will succeed in running content more than those just looking to join groups. Their ilvl will thus rise faster. Most will organizers try to improve subsequent success and 'smoothness' of the runs by putting their higher ilvl requirements for their group, attracting just the players that can meet the criteria as well. Thus nearly all group organizers join a subset of the player-base that accelerate 'ahead' of a very large group of players that do not organize groups, leaving the latter uncatered for. One could argue these people should 'just start their own group', but there are many psychological/sociological reasons why this is not an option for most.
So what could be improved?
Most certainly the 'active' part of the submission could be changed. Let people the option to just select the content they wish to queue for, and get on with their game play, rather than forcing them to keep submitting applications to specific groups and facing long bouts of rejections. The system could indicate a prediction based on the request and the player profile of how long the queue could last.
For the organizer, give the option to accept a 'suggested group', indicating a machine predicted chance of success for the group, rather than forcing them to select each individual player based on ilvl. While certainly a lot of raid leaders will still whittle out the weaker links in the proposed group, or make room for paid carries, the 'lazy' option should be available to just accept the group with a reasonable predicted success option.
Worst case: for the applicant the 'queue never pops', but at least you can play in the meantime, for the organizer worst case you ignore the system and still handcraft the group.