I suppose it comes down to preference. In something situational like PvP I don't think Accession being a GCD is inherently worse (unlike in PvE where everything is scripted and the perfect GCD usage can be mapped out for the entire fight).
Both Excog and Accession bring some contextual factors to the table that might make one preferrable over the other in certain situations.
For example, whereas I see your point with Excog's auto trigger, the Excog effect is only applied to people who stand within the ground circle when you place it, which spans 10y.
Accession is 15y though.
When you manually trigger Consolation it's also tied to Seraph's position. If the center of the fight moves too far away from Seraph it will decrease her impact.
With Accession you are basically a walking Excog and Consolation rolled in one, have better control when and where to activate it and can reach players with your heal that might not have been close to you when you initially cast your LB.
Even though you sacrifice a GCD of your 8k AoE attack for it, you are still doing more damage overall than you would before, where you could only cast single target broil I think?
On the flipside it also makes you more vulnerable because you'll have to be closer to the fight. Being able to place Seraph on a contested checkpoint while you are outside of the danger zone is a perk the old LB had.
I also see your point of stacking Adlo on top of Excog but here too I think the difference is more down to preference because the heals are shifted. Before 7.0 you could tank bigger hits with Adlo's 9k shield + your 8k Excog auto heal, that’s definitely true. You could then use Consolation for smaller damage.
Now recitation Adlo can be used to pad your team against smaller hits in advance with its 8k shield and you can use Accession as your big burst heal to remedy bigger hits.
So basically SCH became more reactive whereas the pre 7.1 focus was on preparation.
So I think SCH's strength just shifted from one scenario to another.
I can totally see though that this can significantly lower someone's enjoyment with the class because the old version encompassed SCH's job fantasy much better whereas Seraphism deviates from it quite a bit (I'm not happy I have to wear angel cosplay in PvP as well now :') ).
With the new LB you are much closer to WHM's style of reactive/post-damage healing whereas the old LB was all about planning.
If you put it like that it’s a shame that the devs sacrificed yet another job fantasy for the sake of streamlining classes. I’m sure there would have been a way to update SCH’s LB without taking the core element of planning and strategizing away. So yeah, that actually sucks.
For players who appreciate this kind of reactive control it's probably an improvement. But for people who prefer a playstyle of planning ahead I can see that the old LB is really better.
Though when it comes to Seraphic flight/nullifying status effects I'd still say the 30y reach is an improvement.

Originally Posted by
AnotherPerson
However, the previous healing spell (Adlo) also have a higher potency
I may be misunderstanding you here but I don't think the old Adlo is that much stronger than the new one? Or are you getting at something else?
(Isn't it like this?: The new Adlo (4k heal + 4k shield = 8k) "only" misses 1k compared to the old one (3k heal + 6k shield = 9k). Together with the damage reduction buff I don't personally see it as being that much worse. And as mentioned above under Recitation both have the same overall value of 12k, since in 7.1 Recitation doubles Adlo's shield (4k heal + 8k) whereas before 7.1 Recitation "only" increased the shield by 50% (3k heal + 9k).)