Is this card nothing but a problem looking for a solution or is it actually a useful strategic tool?

Lets look at what corps typically spend doing:

1. Melange Mining Corp. - Preventing this is annoying, but won't cause them to shed any tears.

2. Purging Viruses - Now we are talking - lets say you've Parasited a big piece of Ice and they've let it tick down to 1 strength, thinking they would purge next turn, what about if you have built up a huge Medium and want to keep hammering them next turn. Even to keep a pair of Imps locked and loaded to wreck their HQ next turn. You can do a bit of damage with this card, assuming they don't have a Cyberdex Virus Suite on hand. What kind of seedy cards can you use to trigger Populist Rally? How about Wyldside, Scrubber or Street Peddler? Sadly Aesop's Pawnshop is too classy to be involved in this populist hoo-ha.

3. Triple Advancing a 3/2 Agenda they just installed in their scoring server. Another interesting situation where you might wish to delay them one turn until you can make your big play for the scoring remote. However Populist Rally will set you back 2, a card and a to delay them one turn. Keep in mind that this is wasted resources if they only installed a Caprice Nisei or Adonis Campaign in that server.

So it looks like there isn't that much that you can do to mess up the corp's plans with Populist Rally. Is it useless?

1. Fisk Investment Seminar then put some more cards in their hand with Leela Patel: Trained Pragmatist or Laramy Fisk: Savvy Investor. Now cut them down to only having on thier turn to deal with being 5 cards over their maximum hand size. They are going to be praying for Jackson Howard. This would be a good time to activate an Eden Shard too.

2. Speaking of the corp's maximum hand size, how about Valencia Estevez: The Angel of Cayambe, Investigative Journalism/Activist Support etc. and Itinerant Protesters? For even more fun you could combine this with Fisk Investment Seminar to really ruin their day.

EDIT for Salsette Island: Taking away a will also prevent the corp from using Jeeves in a lot of cases.

So it might not be practical most of the time, but this DOES stack. That means you can play two of them to stop a predicted "Advance, Advance, Score" (e.g. on a suspected IAA'd 4/2) or three of them to cancel the Corp's clicks entirely (at the cost of most or all of your own though, so outside of specific situations mostly involving extra Runner clicks it's not worth it)

This aside, you can also stop a predicted fast advance with just one copy which can be game-changing if you can snipe the prospective Agenda from HQ and/or the game is currently tied up at 6/6 and you need another turn to try and squeeze a point out of somewhere. Populist Rally can give you confidence that they won't score out next turn, and combined with any Event recursion you can create a Clot style effect that locks out fast advance but without the option to purge.

Or you could just run this alongside Clot to prevent them from purging it! Either option is fine, although this by itself is much more limited against FA but costs no influence in return. If you generally just find yourself needing to squeeze out one or two more turns against FA and can't spare the influence for Clot, it can be very valuable.

Finally, it makes it harder for the Corp to flatline you using something like SEA/Scorch/Scorch. For 2 creds and a click, you can stop worrying about that until next turn. This can give you time to win, find protection, hit HQ with an Imp to get the SEA Source out of there, or even just let you make a run this turn without fear of death (since next turn you can simply not run in order to avoid SEA Source)

Essentially, denying the corp a click denies them options which might have been very painful for you. It's relatively versatile and hedges out some very bad outcomes, offering you a sense of security in whatever else you're doing this turn.

Bloo Moose, our favorite martian fortress, is the prefect place to hold your Populist Rally. If you are just a few creds short from breaking into that scary server and you smell a GFI on the horizon, play this and build up some more before you make a run. Also works deviously well with various Viruses, and also prevents Jeeves Model Bioroids shenanigans. Pretty good, I reckon.