I struggle with removing FKs as a general idea. It's presented in a piece from a developer. It appears to me that if you do this, you are merely moving the problem, and potentially causing other issues. Apart from Grant's response on performance, which is very true, there are other challenges with microservices and separate databases for each service.

Let's say we are doing something trivial, like a simple e-commerce site. I could have a separate database for products, one for orders, one for shipping actions, one for customers, etc. However as I scale, I'm not using intra-database queries or FKs/joins/other techniques to verify information for an order. Now I'm sending messages. At small scale, these are trivial. At large scale, my network traffic and messaging is vastly growing and potentially a bottleneck.

Also, since there is a "products" database, and an "orders" database and a "customers" database, I still can't necessarily scale out these microservices beyond their own machine. Perhaps I can scale them higher in terms of each being as large a machine as I can have now with a single Oracle/SQL Server/MySQL/etc. box, but I'm still have a scaling issue. I also now have a new messaging problem I need to manage and architect. If I lose one database, how gracefully can my application degrade or does it start to fail with unforeseen interactions? Do I create more frustration when customers cannot place an order because we can't find the customer db or because the site is down?

Certainly there are domains of problems that would work fine here. Spotify is probably a good example of this. There may be e-commerce systems that allow this, perhaps being willing to notify customers after some time (hopefully minutes, perhaps hours) that a product is out of stock because the message from the orders database didn't get to the application. There are certainly ways to copy and replicate some  data, assuming that "fresh enough" works for your application. However that's a business decision more than a coding decision. This also means that you also have a new load on your system to move data. I also think the more you work with singleton rows and single objects in an application context, the less you need RDBMS capabilities.

Ultimately I think FKs and strong RDBMS systems work very well in many situations. They work less well in many situations and your domain may qualify for those areas where a NoSQL, a multi-db, or other architecture works. We should certainly investigate and write about where things work and don't work, but I wouldn't assume the RDBMS with it's PKs and FKs isn't a valid, well thought out and incredibly useful architecture.