Pretending Addersgall's timegating is an issue feels a bit silly. I can't think of a single situation/mechanic that scholar could handle that sage would be incapable of (unless it involves moving your party out of AoEs using expedient).
Sch gets all their aetherflow charges at once sure, but if you poorly manage your aetherflow you'll be stuck with nothing for the next 45~ seconds unless you wanna use dissipate. That gives good sch players more control, but also gives weaker players more opportunity to fuck themselves over if they aren't careful. It's a blessing and a curse both.
Sage is more limited, but it just shifts charge usage windows and requires the player to manage them in a different way. Rhizo and dissipation complicate things, but sage players don't have to balance using their addergall for damage too. Overall sages will have fewer charge-OGCD uses, but generally the addersgall OGCDs are strictly better than their aetherflow counterparts (for instance, compare sacred soil and kerachole). Plus, even ignoring addersgall entirely, the other sage tools are pretty great.
As for a lack of OGCD dps tools, I don't think a 45s cd (in the case of assize) adds all that much to the playstyle.
TLDR; Hell nah.
I didn't say Addersgall is an issue, or suggest that there is any content Sage can't do. I implied Sage doesn't have as easy a time dealing with the situation of having to forcepull a party of shitters through a dungeon, which is an unintended (but sadly not uncommon) situation SCH happens to have an edge in. My point in making the comparison was to illustrate that SCH doesn't
need Eos casting Embrace every GCD (though you can force her to) to heal a dungeon competently, but I'll elaborate.
SCH can access more OGCD heals at once if they need to, that is a fact. If you start with 3 AF, with Aetherflow coming off cooldown, and Dissipation, plus Recitation, you can blow through 10 Aetherflow skills in a row if you need to and never have to stop casting Art of War. If you want to be realistic and assume you're out of AF at the start, that's still 7 such skills.
Sage can only hold 4 Addersgall at a time max if you count Rhizomata, and can only recover one at a time. Scholar, on the other hand, has the luxury of being able to choose if it wants to blow its Aetherflow all at once or keep some/all of it, and has more available charges to do so with. To be clear, this is not optimal Scholar play, however it is key when you have a tank with whose HP you have to play ping pong.
If you aren't in a party of exceptional individuals, Sage has more than enough tools to handle its role, do strong DPS and excel. If you have a party with a tank that doesn't know what Rampart is and two dps that don't have aoe on their bars, Sage can handle it, sure, but it sucks even more than it does for SCH. That's all I'm saying.
Incidentally, you ought to be using Dissipate. It's free Aetherflow and easy access to a thick Adlo shield for your tank. Pop it when you've used all your fairy cooldowns and the pull is winding down. Eos will be back up by the time you need her again.