While that set certainly seems usable if only for the utility of TR + Imprison, Trick Room teams are few and far apart in the current doubles metagame, reducing the effectiveness of such a set. In addition, Azelf's defenses are mediocre at best, even with maximum HP, and since Imprison is only active as long as the user is alive on the field, even if it can get a surprise Imprison up the first turn, it won't be the best selection to continue to make Trick Room unusable, and due to the extreme bulk of many Trick Room users, such as Cresselia or Eviolite Dusclops, Trick Room users can easily stay in the match for the couple of turns or so that Azelf will stay alive, and then set up TR, especially as they won't have to worry about attacks from two Pokemon at once, since that set is geared toward a supporting role and deals little damage.
While the concept may be sound, I feel it's outclassed by Imprison Chandelure, which, despite its greater number of weaknesses, is far bulkier than Azelf, and most importantly, can use its STAB Shadow Ball to hit common Trick Room users quite hard, 2HKOing the vast majority of them. It also has the ever-useful Heat Wave. So while the set is a good and useful idea, in practice it's not going to make an excellent doubles partner, even for the precise niche it does possess. That's not to say the idea is itself useless, and in fact I can see an offensive set with Imprison + TR and two attacks retaining some of Azelf's utility as an attacker while also preserving that niche as a "surprise" TR stopper, but it will have the same issues with frailty as the first set, and having only two attacking options somewhat limits its coverage.
As for why Azelf receives such little usage in Double Battles, I think it's really because most of what it can do is outclassed by something else. If you need a fast and powerful physical attacker, Garchomp exists, and its spread damaging EQ and huge bulk make it rather more useful than Azelf. Thundurus outclasses it as a special attacker, with better coverage and access to Prankster to abuse Substitute, Taunt, or Thunder Wave. If you just need something fast, Choice Scarf users, weather attackers, and Pokemon such as Weavile do that better due to their superior Speed, and in many cases power as well. In doubles, I don't really know if Azelf has a specific niche that nothing else can do better, which is why it's not used very much.