Should the company require employee pictures on the company directory?

The problem, it is a big company with lots of people...

...Am I being unreasonable asking that their directory or MS Teams picture be of them, not something they find amusing?

You can ask HR if there is a policy (there can be a policy and you don't know it or it isn't enforced). If there isn't a policy you can suggest that they should have a policy and you can suggest what the policy should be. If they have a policy and you want it changed, then you can suggest it.

I have seen several policies over the years:

• No policy.
• Almost anything goes. Most people can do what they want. Though I imagine public relations people, senior leaders, and sales might have a specific set of rules.
• No pictures or anything else. Just the generic symbol.
• The company makes everybody use the picture from their badge.

Unless you know the company policy, and you are in a position of leadership over the people you ask; you can't require another employee to use a specific type of graphic.

Am I being unreasonable asking that their directory or MS Teams picture be of them, not something they find amusing?

In virtually any case, yes, it's unreasonable. As others have stated, this is matter of company policy and apparently your company is ok with the status quo. So, if "they" are your peers, they don't have any obligation toward you. If they are up in the hierarchy, obviously it's inappropriate. If they report to you, they could simply ask you why they have to while others are free to show their pet.

Having said that, your need is totally legit and you can do something about it:

• You can set the example (as you are doing) and maybe you could be even more explicit, by for instance adding your picture to your email signature or something equivalent.
• You can ask to have more virtual meetings with your colleagues. Sure, it's fine to work offline, but in some moments is very efficient to work together. You put your camera on during these meetings.
• Find reasons to have joint live sessions if you are working on the same project. Ask to visit X's office as soon as it is justified from a business point of view and enjoy a nice long working session with them.
• Go to your office more often, if you work from home in some capacity.

It is a known fact that people can cooperate better AFTER they have met face to face at least once. And having a picture of yourself in the corporate directory is a small step towards that - make people feel a kind of personal relation, to improve the corporate communication.

From Wikipedia (thank you @IgorG for helping)

"Another study found that face-to-face communication is very important in building an effective team environment [https://doi.org/10.1108%2F13527590610652774]"

And from the abstract of the linked article:

"Practical implications [...] include attention to the selection of leaders, continued facilitation of face‐to‐face communication in a virtual age and investment in language and intercultural training"

The downside is that many people these days are inclined towards abusing what is available in various ways, from the simple sharing of the photo, to downright using the photo for illegal purposes. And that is one of the main reasons why NOT to have one's picture readily available.

With this information in mind, I lived with this inner "conflict" for quite many years already, of whether it is better to have the pictures in the corporate profiles or not, and the conclusion is simple: it is impossible to answer with a simple yes or no. I admire the colleagues who actually share pictures of themselves, and I do not accuse the colleagues who prefer to remain "private".

I had the experience myself, that even if I worked well, remotely, with some colleagues, everything improved drastically after we had the opportunity to meet personally and spend some time together. This is why I recommend people to meet face to face at least one time, if possible, if they will need to work together from remote locations. Not only communication, but the entire experience is going to benefit greatly.

This isn't making any sense. when we take this

We talk every few days over MS Teams but almost never with videochat because we have work documents to discuss

and then juxtapose it with this

When I talk to a people, it is good to have at least some idea what they look like

Instead of making this an issue over employee pictures in the company directory, wouldn't it just be easier to turn your camera on? Certainly there is not company policy against doing that. You don't have to involve HR. Even if you are sharing documents, you can start your meetings looking face-to-face by camera, and share the documents when you need to, and go back to the camera when you don't need to share the documents.

If I were your HR person and you approached me with such a proposal as you're stating here (especially with nary a notion on whose job it would be to enforce such an idea), I would look at you with... a "questioning eye" (to phrase it nicely).

Good grief!