This type of service has existed long before ecommerce. Brick and mortar retailers pay someone to go to stores and check prices.
How are you missing the subtle shift that makes this not the same?
If I ran a bakery, say, in New York City in 1900, I could send a boy around to the nearest five bakeries and get answers within an hour. That would be "real time" within that context, in the sense that customers would not respond faster than I could gather the information.
If I ran a stall at a market in, say, 1500s England, selling potatoes, I would know what price my competitors were selling potatoes for, faster even than an hour.
If I ran a gas station at an intersection, I could see at a glance what price my competitor across the street is displaying.
With current stock market tools, I can see the backlog of both buy and sell orders.
When I go to sell a house, my agent tells me the asking prices of comparable houses that are currently for sale, as well as the actual selling prices of comparable houses that have recently sold.
This is how markets are. Sellers know each others' prices.
So the only thing different is your "grabbing coffee afterwards" claim, and so far, I have seen nothing of substance to back it.
The same thing has happened in many markets. Quicker information results in more accurate pricing and lower risk, which translates into efficiency and less dead weight loss.
More accurate prices for suppliers means they can produce with less capital risk, which is generally also good for consumers since the consumers don't have to pay more to give the supplier as large a safety cushion. This has been historically true, it's basic economics, and it's empirically true in the literature.
Think if you produce a product, and there's a lot of risk in your supply chain. You need to charge more for your end product to account for that risk. This can be and is measured.
Remove risk (whether it's credit, inflation, pricing, stability, etc.), and the supplier has less risk.
This is never purely going to profits, since your competitors generally also have the same risk landscape. So any gains perhaps help profits, but some are also used in other sectors of the business - selling cheaper to try and grab market share, better wages to attract better employees, and so on.
> if the competitors can lower it nearly at the same time and you get negligeable additional sales
If you and all your competitors lower prices then likely more of the entire sector of products makes more sales as more people can afford the product. This has been the pattern since the original Luddites - when textile prices dropped from automation the entire sector exploded and produced around 10x as many goods. This too has been the pattern across history and industries.