SMS and MMS can, by design, only work under very low bandwidth conditions. That's why you can still send/receive them even if you disable WiFi and mobile data, texting only requires is basic cellular connectivity. As far as sending photos and videos via texting, depending on the carriers they will either scale down higher resolution photos and videos to meet their arbitrarily set file size limitations (most under 1 MB), or you just see some kind of '...undelivered...' error message.For photos that might not be noticeable unless you're viewing the texting version and the original at the same time but for videos the scaled down versions are typically pretty blurry. Email is often a much better option for exchanging photos and video -- Gmail has a 25 MB file size limit for attachments, Outlook is 20 MB but much, much larger if OneDrive is part of the process. Which leads to the other good way to exchange files, by just sharing links to files stored in Google Drive, OneDrive, Dropbox, SpiderOak, etc.
Regarding services like Apple's iMessage or WhatsApp that rely on proprietary protocols, note that users in each environment can freely exchange files but only between themselves. When someone using iMessage is sending a video to a non-iMessage user, the message itself has to be MMS, on the default iMessage format, so on the receiving end, again depending on the whims of whichever carrier, the video may be scaled down or not even included.