Because Attack Speed, Movement Speed, and Sustainability are crap on a hero like PA? Honestly all you really need is Drums + BKB and you're very survivable. Dominator is no more helpful for outright survivability if you're going to worry about exclusively getting nuked down. It's hardly a garbage item.
Sorry for late reply, I was asleep. The reason the attack speed and movement speed are not useful is that you have to thing about what PAs strengths and weaknesses are, and how you will play because of this. Drums is an early game item, through and through. On most heroes the attack speed and movement helps you chase and gives you more dps. But PA has a 50% slow with 75% uptime, and a long range blink with low cooldown. She doesn't need more chase. Additionally, whilst PA is being played as a mid-game carry in this situation, she is still a carry. She needs to stay well away from the front line during fights early on, as nukes will destroy her. Instead you should be waiting for the fight to break down, then blinking on targets trying to rotate out of the fight on low health. Hence, you should be attacking only because you blinked on someone. This gives attack speed, so the drums attack speed is unnecessary. It will give you a tiny amount more dps but with only 1 item the effect is negligible.
Helm, as I mentioned, is a farming item, I only get it first if I will not be fighting much and need to sustain being in the jungle a lot. So yes, I agree it doesn't make you much tankier. But drums gives you 200 hp roughly, which is not gonna save PA if you are getting focused, as her hp is so fucking low that it means you survive 1 more magic missile, hooray.
BKB is something I don't like being forced to buy first either. I get it when the game is going to shit, and I simply have to go on the frontlines a bit for my team, so I need to survive the aforementioned stuns and nukes. Otherwise I get it second or even third if they have like no cc at all hardly.
I like basher first as it gives you more damage and the ability to lockdown targets early. It is also a long term investment for you abyssal, which is a fantastic mid game item on PA. with basher you can jump on someone, hopefully get a crit and burst them down, then get out. You can also solo kill with basher if you find some poor support somewhere.
When you have all 3 of these items, you have reasonable damage thanks to phase basher and BKB, enough to make the lifesteal do something in fights. You should also have a few points in blur by now, so evasion plus magic immunity should make you very survivable. And basher gives you proper lockdown in a manfight. These factors combined allow you to start going on the frontlines and start properly carrying. And by that point, the effect of drums will be neglagible. All drums does is delay this holy trinity, which is a horrible idea, as PA needs it ASAP to impact the game as much as she can before MKBs start coming out, at which point her survivability vs the other carry goes out the window. This is as much detail as I'll go into on mobile.