> Some of them have coupons to specific items that are not allowed to have sales prices lower than the MSRP.

That's actually kinda disappointing. I'd always assumed those flyers were pieces of trash (at best, something I'd need to put in a recycling bin) which I don't want but now I'll be more tempted to take them when offered on the chance that I otherwise accidentally avoid the sales price.

It's still good to know that such coupons are likely just attempts by the retailer to circumvent the manufacturer's... ahem suggested price.

Coupons are a longstanding price discrimination technique. If somebody doesn't want to pay full price, you might still get their custom with a voucher. You don't want to make the discount too easy to find though, as you will miss out on revenue from people who were willing to pay full price.

ProTip: at some stores, employees are allowed to give discounts as well. i have 2 anecdotes from HomeDepot:

Since none of their lumber should ever be in the same building as the word "straight", I made a joke to a nearby employee that we should get a discount at how warped the wood was. He very seriously told me to separate the warped wood on my cart, and he'd mark them down. Got to the register, and they were marked down 40%.

Second instance was after spending time chatting with an employee in the appliances department, he pulled out a pre-printed, handcut piece of paper from his apron pocket, wrote 10% on it with his sharpie, and i got 10% off at the register.

Oh, and of course the Guitar Center stories of "you're a cool dude, and since I like you, let me knock of X%" are infamous