plus, the next round of people start to believe that such a hechsher is required, since the Eidah provides it...

I was once at a symposium where a prominent Rav who gives hechesherim. He was explaining that oils that are liquid at ambient temperatures like olive oil, chestnut oil, sunflower oil, etc. (contrasting with solid oils like palm oil) can only be processed in specific machines that only process kosher oils so there is no need for a hechsher. Someone then asked him why he gives hechsherim on such oils. He answered: "The factory owner asks me to certify that his oil is kosher, which it obviously is. I have no legitimate reason to deny my certification. But I repeat that similar oils without hechsherim as just as kosher."

Does the BAdatz bleach really cost more?

It does necessarily have to, as the additional overhead of the heksher will be offset by additional sales.

Leave it to the kashrut companies to kind of confirm the "kosher tax" canard, which may not be such a canard after all.

SD, I don't know about in Israel, but here in the Malchut Shel Chesed, all kosher grocery stores are in general more expensive. They charge more for meat (of course) and they also charge more for tissues. Since most people don't have the time to pick through the items in a regular grocery store, and many people enjoy supporting a shomer shabbat store, they patronize these stores, and they pay more overall. The ticket of entry to being stocked in these stores - especially around Pesach time? A kosher symbol.

I dont know if bleach specifically costs more with the Badatz than without, but overall, as said above, most kosher items are more expensive than non-kosher items. And in Israel, most items with mehadrin hechsherim are more expensive than similar items with regular hechsherim.
maybe it does not need to be more expensive, but they definitely charge more.

This is standard policy for pretty much every hashgachah I know of, whether small or large. All of them rely on providing hashgachos for their income - so if a company says to them, "Come visit us and confirm that our product is kosher," they do it.

I understand the argument that larger agencies are 'trendsetters' for the community, so that the moment I see a bleach with hashgachah, I am less likely to buy a bleach that lacks it. But I'm not sure it's fair to lay the blame for that at the feet of the hashgachah agency.

Josh is correct. The problem isn't today, but rather in 50 or 100 years from now. In 50 or 100 years, people will look back and see that their great-grandparents hakedoshim had a hashgacha on their cleaning supplies and due to yored doros, they are definitely required to have a hashgacha on cleaning supplies and a special Pesach hashgacha for a month before and during Pesach.

It is a chumra that is absolutely not necessary.

Why is buying bleach with a hechsher considered a chumra? Just because it's restrictive, it doesn't mean it's a chumra. (Would you consider some other arbitrary restriction, such as only washing your towels on Thursdays, to be a chumra?)

By labeling this ridiculous practice with a word generally reserved for venerable practices, you're perpetuating the problem.

The eida hacharedit has a special symbol for non food products that don't require a hechsher it says bIshur habadatz instead of bhashgachat habadatz.
I would imagine that the cost for the ishur is minimal. And for people who don't know it is probably more convenient to look for the ishur instead of consulting a list of products that don't require hechsher. However, with things like bleach and toilet cleaner where it should be so obvious I think that it going way too far.

I don’t think that the issue is the extra price, which is at most a few agurot per product (in any case the difference in price can greatly vary between the different supermarkets and makolets.)
But the problem is more the “zilzul” (scorn, disdain) that it causes - even amongst observant Jews (all the more so amongst traditional or non-religious) regarding kashrus and religion in general. Most people look at the hechsher on cleaning detergent and think that “the rabbis are just squeezing out more money for something that is unnecssesary.” If Badatz gives a hechsher to toilet cleaner, tissues, plastic tablecloths, soap and shampoo – than it just proves that “all hechsherim are a farce” and this cynical attitude will just be encouraged for food products as well. (The differentiation between a Hechsher and Be’ishur is irrelavent.)
This is all in addition to the idea that having such a hechsher is not Emes (untruthful. i.e. false) and belittling the Torah and the halacha.

As a previous commenter said, the Badatz uses a special hechsher for such products, where they write Be'ishur HaBadatz -- approved by the Badatz -- instead of Be'hechsher HaBadatz. I think such language makes it clear that this is not something that requires a Hechsher per se, but just the opposite, the Badatz has approved this for use on Pesach despite the lack of supervision.

The halachot for what doesn't require a hechsher a bit more complicated that one thinks -- for example, even poisonous, non-edible products can be chametz according to some authorities under certain circumstances (i.e. it is a liquid) -- and so I can even see why confused consumers, whether ba'alei teshuva, or even many veteran Pesach shoppers who forget from year to year, would find such a seal welcome.

There's always another side to every story. While I am obviously not aligned with the Badatz, they are talmidei chachamim and I do not think they are money-hungry Halacha-twisters.