If consumers lack the moral conciousness on their day to day transactions, then how can we expect them to make the right moral choices when they vote?
There have in fact been successful consumer-led movements, but the most successful of these concern cases where the consumers also happened to be the same people being exploited (colonial India's rejection of dumped British textiles, the Montgomery bus boycott, the Boston tea party, etc).
Cases where consumers have acted en masse on behalf of another exploited class are a lot fewer and weaker. To some extent, one may point to the current growth of organic animal products as an example of this, but even in this case, this has been boosted by consumers seeing these choices (in some cases rightly, in some wrongly) as also healthier for human end consumers besides the question of animal cruelty.
History's guide suggests that while morally-minded consumers can and should vote with their wallets, such personal virtuous choices are largely useless without a larger movement to effect change.
And if history suggests that people's virtuous choices are largely useless, then how is their voting going to be any better?
A more topical one might be if you disagree with a company using sweatshop labor. Figuring out which companies engage in sweatshop labor and avoiding them is a remarkably difficult task, not in the least because companies do whatever they can in order to hide said actions. And even if you do manage to create a list of good/bad companies, there's no guarantee that you can purchase solely from the good companies without having to go through some other morally dubious medium such as Amazon.
The idea of shopping based on your moral conscious might've worked 50 years ago when the supply chain was far smaller, but nowadays it's so complex as to be almost unfathomable for one user to shop their moral compass without touching at least one thing they disagree with.
With regards to the sweatshop labor: if you care not to buy sweatshop clothes and you can't reasonably establish the origins of the clothes, then don't buy them. Only stick with manufacturers who have had their products verified by a trusted third party.
It's also overly reductive and ignores things like voter suppression, extralegal affairs and abusing the court system.
For your second argument, you seemed to ignore my original point which is that it's generally impossible to actually establish the origin of said clothing due to the complex supply chain behind the scenes. Even if it's a trusted third party, that clothing is still being delivered via companies that deliver sweatshop clothing and sold in stores which sell sweatshop clothing. At a certain point some percentage of what you pay will go to support said sweatshops whether directly or indirectly, so how can you expect a consumer to operate in a full moralistic behavior when all of their actions are losses? At that point the only winning move is to not play, which is also not possible because, well, Capitalism.
Given how many people actually don't even bother to vote, I doubt voter suppression is the problem. It seems like an issue of implementation and limitation of the current political system. In contrast, "voter" turnout by consumers is 100%. Every product you buy is a vote you cast.
With regards to tracing the origins of a product: you're trying to fix a problem that's even worse with government. If you're so concerned that you aren't able to identify the origins of a product with 100% certainty, then we ought to compare it with the baseline: what is the trust factor with government? At any rate, the traceability of a product can get as accurate as you want it to be... so long as you pay enough money to establish it. If you want, you can be flown to every part of the world and you can personally ensure that every fiber of your clothes is not coming from a sweatshop. Of course, that would be insanely expensive, but it is possible. 99.99999999999% of consumers don't want that much transparency.