Plans? What you are asking is more of an app developer question. Verizon sells cellphone service, they don't develop apps.
The existing plans are what they are. The software has to be capable of transmitting information privately and received privately. It seems a matter of each users security, not an app, plan or phone issue.
I assume Verizon either directly develops or has control over the development of their Verizon Messages app - which is what I was referencing. Based on your responses of security, it's clear you don't know what end-to-end encryption is nor why it is important.
The type of encryption I'm requesting prevents Verizon or other parties, other than the intended recipient of a message, from viewing the contents of the message. Verizon Messages offers no encryption outside of whatever encryption is inherent to the carrier signal.
There are various reason why end-to-end is superior. I asked the appropriate question in the appropriate part of the forum.
Any message sent with data only, like Facebook messenger (or any data driven text app), is completely unknown to your cell carrier. It's data. They don't even know it's Facebook. It falls on your bill as "social media"
Is there some other reason to need encryption?
This is patently untrue. Unless the application implements some sort of encryption or VPN, everything you send is viewable by the ISP (in this case it's your carrier - Verizon). They also would absolutely know it is Facebook, unless again, you're using a VPN (mere encryption doesn't hide the destination). I'm sorry, but you don't appear to have a basic understanding of networking or even information security in general. What you believe is just utterly wrong.
The major reason is for sheer privacy. I don't want Verizon to know what I am doing. I don't want Facebook to know (they implemented their Whisper protocol based "Secret Chats" which is secure across Verizon and Facebook, but requires the recipient to also use Facebook Messenger). A Verizon Messages solution would potentially be able to implement the same protocol and allow some form of compatibility, allowing those who don't use Verizon Messages to interact with those who do in a secure, private fashion.
You are contradicting yourself.
FB messenger is sent as data, not SMS. (Unless you allow FB Messenger a as your SMS app)
The content of data only messaging is not know to your carrier. If you look at your bill, your carrier will report data use in broad categories, like web browsing, social media, video, audio. The actual content is not known, nor is your carrier legally allowed to poke into your content.
If you replace your native messengine app with FB, it is sending as SMS and data, similar to iMessage, depending on if the other in the conversation has FB messenger.
Carrier messaging is obviously not secure. It is backed up and synced across compatible devices. That doesn't mean carrier knows or shares the content.
As for your need for privacy, I've said it before, if you aren't doing anything wrong, nobody cares what in your messages. If you are, then what do you have to worry about.
I am not contradicting yourself. I feel like I've said this multiple times, but I will make it very clear to you:
1) SMS IS data from a network perspective. It's a stateless communications protocol. Your point about how it is billed is irrelevant to the network side of the discussion. Again, it is ALL data and how Verizon labels and bill for it is just a business decision, not a technological one.
2) Verizon can absolutely "peer" into any data, unless that data is encrypted and even then, depending on the method of encryption it is possible for Verizon to break that encryption (MITM attack of a SSL session negotiation, for example). In fact, they have been injecting third-party trackers into customer web browsing activity. Please see this EFF article: Hold Verizon Accountable for Violating Its Users' Privacy | EFF Action Center
3) End-to-end encryption prevents any parties (carrier, application provider, etc) from viewing data...only the intended recipient should be able to read it. That means no Verizon, no Facebook (even if using Facebook Messenger - which happens when you use a "Secret Chat"), no government, no one can easily view your data.
"As for your need for privacy, I've said it before, if you aren't doing anything wrong, nobody cares what in your messages. If you are, then what do you have to worry about."
That is simply not your call to make and, frankly, my belief or reasoning behind why I want privacy is not up for discussion or debate. Your opinions to the contrary are irrelevant to me and my concerns.