Is there value in "Non-Disclosure Agreements (NDAs)? When you want to look at a demo, conduct a POC, or even purchase a solution, I mean, do they create a false sense of security? Are there many cases of people enforcing them? Maybe there is an easier way to go about it? It costs a lot of money and often requires a significant amount of time as well.

NDAs have given way to Mutual NDA barring a few big vendors who still want you to sign their version of NDA.

With every discussion with a new partner, I have always insisted on a mNDA to safeguard interests on both sides. When we share non-public information with any new partner we want it to stay out of public view; it could have material impact on share price, company reputation, or simply open up the entire landscape of vendors knocking on your doors to sell what they believe is the solution to the problem/opportunity.

Many times, we do not only sign an NDA with a vendor but instead use a Mutual NDA form to protect both side.

Sometimes, vendors are touring the market with their products, hence presenting them to our competition.   We don't want anyone hear from what we're doing as it could even be sensitive internally.

In the past, as we are a very large organization, we've seen some vendors working a POC with one team, going to another team and discussing about the POC they were doing.

That's how we ended up having a MNDA agreement signed.   It's to keep things in a small circle.

Have we ever had/applied sanctions because the NDA/MNDA was broken?  Don't think so.   But it clearly gives levers to procurement.

NDAs are there to protect intellectual properties/innovative ideas. Just like when I get a good idea that requires some kind of outsourcing, and I would not like to find it executed by someone I went to for help.
Personally, I do not find them counterproductive because they are just like the rough sketch. Until a solid valid contract has been signed, I do not worry about changing processes or designs.
In any case, the opinions vary depending on past or current experiences.

Yes, there is value. I don't believe it creates a false sense of security at all. 

Think about what will happened without the NDA. Vendors will be freely to disclose what tools you are using, your POC results, your weakness or even your internal politics. You will find the NDA critical if you think this way.