Reports last month that (NASDAQ:AMZN) had signed leases for its new grocery store chain that is separate from Whole Foods failed to disturb its rivals in the way that prior announcements of its moves into physical retail have.

While that's partly because the original news about the new-concept chain was first released earlier in the year, it's also because many of its rivals may not seem to fear Amazon's presence as they once might have.

Brick-and-mortar retail is proving more of a challenge to Amazon than many thought it would, and grocers like Walmart (NYSE:WMT) and Kroger are well fortified to resist an assault on their position.

A whole new world

The Wall Street Journal reported that Amazon had signed more than a dozen leases for new supermarkets in the Los Angeles area alone, and it plans to open in Chicago and Philadelphia, too. Because it wants to expand its reach with customers, it wants a chain of grocery stores in major metropolitan markets all across the country.

Amazon's acquisition of Whole Foods Market in 2017 shook the food industry -- from supermarkets to consumer packaged-goods companies -- as everyone feared having to square off directly against the online retailer. Shares of Kroger and Target both dipped, and smaller operators such as Sprouts Farmers Markets and Ingles Markets saw their stocks plummet on the news.

Two years later, though, Amazon's positioning for a relative imminent opening of new stores barely causes a ripple. Undoubtedly smaller chains still need to be concerned because the supermarket business already operates on very narrow margins, but there's no reason for the grocery giants to worry, at least not yet.

A constantly evolving strategy

Amazon still needs to work out the kinks of how to operate in the physical retail space. Despite growing its base of Whole Foods stores to 505, and adding a dozen or more specialty retail stores, physical retail sales for Amazon of $4.19 billion are 1.3% lower than a year ago, and 7% below where they were when it acquired the organic grocer.

It may speak to the bad shape Whole Foods was in when it was acquired, and Amazon did close down the discount 365 chain, too, but it has two dozen or so specialty stores, and none are really moving the needle.

At the same time, Walmart has successfully bridged the gap between its online and analog operations, allowing customers to seamlessly move from one to the other and back again. Convenient pickup and delivery options now give Walmart consumers flexibility in how they want to shop, whether online or in its stores. And its everyday low-price strategy remains perhaps the biggest draw for consumers.

It is providing an effective counterweight to Amazon online that is forcing the e-commerce giant to make moves that hurt its bottom line.

The high cost of retail

Having reduced delivery times for online orders from two days to one for its Prime loyalty program members, Amazon saw profit growth slow in the second quarter as earnings came in at $2.1 billion, or $4.23 per share, down from $2.9 billion a year ago, and badly missing expectations. Now that it has made the AmazonFresh grocery delivery service free for Prime members, profits potentially will be pressured even further.

Amazon is famous for forsaking profits for volume, but the grocery wars are different, and it looks more like Amazon is the one under pressure, being forced to build out an expensive physical footprint while forgoing profits, unlike its big retail rivals.

There may come a time that Amazon learns to navigate the analog retail ropes, but it has not yet proved capable. And with Walmart, Target, and others occupying the space, supermarkets don't yet have to worry about a new grocery store from Amazon.

This article originally appeared in the Motley Fool.

Rich Duprey has no position in any of the stocks mentioned. The Motley Fool owns shares of and recommends Amazon. The Motley Fool has a disclosure policy.