I’m in agreement with others, more plastic is generally not a good thing. In terms of conservation, I wonder if the laminate material protects the postcard from UV breakdown.
I stray from the topic a bit here, but believe this is pertinent:
While the original poster was asking about cards already received, some have mentioned sending or receiving cards that have been laminated or are in a plastic sleeve. I’ve received a card in a sleeve or two myself. I would note that, at least un the U.S.A, the United States Postal Service (USPS) has very strict rules about this. Stamps have to be on the “outside” of whatever is being sent, so that they can get cancelled and mail fraud is avoided. Put another way, the ink from the cancellation has to be applied directly to the surface of the postage stamp.
Additionally, pretty much all mail here is machine sorted. Mail (and in particular postcards) that will not process correctly through these machines (this includes square pieces of mail, by the way), or has the potential to harm the machines is not permitted. This is referred to by the USPS as “non-machinable” and there is a surcharge for that, meaning additional postage is required and has to be placed on the piece of mail. Here’s an article for how that works:
https://faq.usps.com/s/article/What-is-the-Non-Machinable-Surcharge-for-First-Class-Mail
Here’s the current non-machinable surcharge stamp:
Note that there is no denomination value printed on the stamp; this means that these act similar to our other “forever” stamps, in that they are always good for whatever the current non-machinable rate is (currently $0.99).
I would also note that some people like to decorate their cards with stickers that are non-two-dimensiona (kind of puffy)l. These violate the rules mentioned above, and often don’t process well (cause the card to get damaged or destroyed). I have nevertheless received some intact over the years, and in fact received a postcard with a wax seal on it intact just two days ago. You never know. I have also received cards like this with a “postage due” notice to collect the non-machinable surcharge.
Apparently the most common scenario in which the USPS seems to deal with non-machineable cards is specialized wedding invitations, either square ones or with was seals or other decorations.