Is a US passport card good or valid id while in Europe?

I carry it every day as my ID. Most people have no idea what it is but is useful if you need to leave an ID.

My passport is in my money belt.

"not worth the effort to carry?"

LOL, it weighs 1/10 of an ounce. Carry it, already!

I found a discussion of the Passport Card as ID overseas in Flyertalk from a few years ago. I hope it's helpful for you.

For what it is worth---

https://travel.state.gov/content/travel/en/passports/apply-renew-passport/card.html

The passport book and passport card are both U.S. passports. If issued for the full validity, they are both proof of your U.S. citizenship and identity.

Presumably its not good for international air travel as there is no way to 'stamp' it, like the passport book.

Legally, it is not valid. No European government has (AFAIK) signed a treaty with the US to accept it. If they were to, they would require the US to accept European ID cards, which is unlikely ever to happen.
Unofficially, private individuals are free to accept (or refuse) anything they want to.

"I believe that the consequences of losing or having a passport card stolen is less severe than having a passport disappear" - not sure I see the difference. In both cases you need to get a new one from the government.
I am not sure what the problem is with carrying your passport as ID. I cross borders most weeks, so I have to.

Presumably its not good for international air travel

That is correct. The link from the State Department you provided above provides that info.

Why can't I use a passport card to fly internationally?

The passport card was designed for the specific needs of northern and
southern U.S. border communities with residents that cross the border
frequently by land. The passport book is the only document approved
for international air travel.

I am not sure what the problem is with carrying your passport as ID. I
cross borders most weeks, so I have to.

I don't understand either.

I was issued this card about ten years ago with my passport . The instructions that accompanied it were clear - it is only valid in place of a passport in Canada and Mexico

It might work for places you have to leave some form of ID like museums when you get a voice guide device. But for any real passport required activity, crossing borders identifying yourself to law enforcement, only the actual passport book will work. Just like it states on the US State Department web site. Wouldn't hurt to carry it as it might work to help identify you if you lose your passport book and have to get a replacement at one of the Consulate offices.

shall I carry this card as my "every day carry" identification and
leave the passport in the hotel, or will it not be recognized as valid
id making it not worth the effort to carry?

There are a lot of answers not related to the actual question. Yes, you can use the Passport Card as an everyday ID, which basically means leaving it for an audioguide or sometimes for a credit card transaction. But other than audioguides, it's pretty rare to need an ID at all.

Not valid at all in Europe. It's only valid for crossing borders into the US from North America (have they expanded it?). Part of what your passport shows is the stamp that confirms you are in the country legally. I'm sure the card would work as a deposit for an audio guide or bike rental, but so does your - much less expensive - drivers license.

There are a lot of answers not related to the actual question. Yes,
you can use the Passport Card as an everyday ID, which basically means
leaving it for an audioguide or sometimes for a credit card
transaction. But other than audioguides, it's pretty rare to need an
ID at all.

I use one of my expired NYC Parks Department annual tennis passes as the form of ID I leave in order to get the Audioguide as it has my photo on it. I would never leave a current form of ID with a museum, castle or any other entity that requires leaving the ID. :-)

If you're not a driver, it's actually somewhat easier to get a passport card to use as official identification than it is to get a Real ID-compliant state ID in many cases. My passport card did not require five different documents verifying I lived where I said I lived, unlike my driver's license, which did.