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I think your analyses of UA vs Tactical support is off. UA is a complete doc with viable tools that support eachother throughout, especially in urban environments. UA works in every map size Tactical Support doesnt have that quality of commander design. Its just an inferiorly designed doctrine. We see Calliopes are highly rated by TS in 4th most popular 4v4 even with poor design. Tactical Support needs a clarification of what it does, which is a weird jumble right now.
UA is actually one of the best situated USF doctrines currently, as its always highly picked but only most picked in 3v3. Its a generally good choice that feeps good (we can't see win rates by commander). Other doctrines should have its clarity and support.
Airborne doc has the highest low-team-size pick rates, and loses the top spots due to a lack of artillery and off-maps (which is why infantry rules big team, its ALL arty and consistent off-maps). Airborne has great thematic design and the tech skip is actually relevant, with one of the potentially (depending on the patch) best alpha strike AT loiters.
Mechanized has dropped out of 1v1 king after the super light vehicle nerf, and will get more clarity next patch with only 1 premium medium choice. It might need a swap out for a proper late game call in to enable team play.
Armor is almost there but all of its abilities were just not quite functional. Dozer dies to the schreck blobs its supposed to counter, 240mm howi is just insanely inconsistent and expensive. The patch really helps here, even if it should just have reduced scatter. 225 muns is friggen expensive for long lead time lottery results. The wolverine and elite vehicle crews dont really do much in team games, as we've beat to death. EVC repairs are redundant with Assault Engineets. Maybe allow EVC as an off map call-in elite CQC unit, or find something else for them to do. Wolverine is a dirt cheap anti armor stalling tool that becomes completely obsolete when heavy armor roles due to its craptastic pen. Its the Armor company not the TD company, swap the wolverine for a premium medium or the Pershing.
Rifle company crutches on the E8, but the E8 comes out when Panthers do without AT supremacy and good AI. It has minimal shock period and lacks the AI to really shock. The patch might give it better AT, but it loses more AI shock period. I predict we wont see much change as Sherman + M36 gets armor sooner and more consitently fights panthers. Replacing Fire Up! with Cover to Cover would make an expensive AoE sprint at least provide smoke. And WP just doesnt threaten late game armor or howitzers or punish slow movement fast enough. Swapping WP for ToT would dramatically improve Rifle usability. Though giving ToT to more doctrines would increase usability.
More clarity of vision, less redundant choices, and more impactful abilities make good commanders well designed. Tactical Support just... doesnt have that.