Hi Ben,
I assume that the visual feedback of the material icons is, more often than not, just sufficient.
If you have hundreds of materials and lost track, you can drag them to a new folder in the Content>Browser>“New Folder”. This lets you search by name. The folder can be deleted at any time.
I have recorded a little clip for you:
https://www.amazon.com/clouddrive/share/7kh0RVyZ4cZlBrwAE5xnTca0MIxVn7xWDPPnmn3msen
A Material to Object is available as well, but yes, you have to have your scene organized (Layer Browser). If the Textures are named more efficiently, you could use the Project Asset Inspector, as a workaround.
More layers, if named in an organized way, should not lead to trouble. Organization, here especially naming conventions, seems to be of little interest (subjective observation over the past 15 years now, answering questions). Well, except for studios, where you follow guidelines, or you’re out. If materials in production are named hierarchically, for example, the A-Z sorting works fine. Perhaps something to consider.
To answer your question: A search option is available in some areas (which means the knowledge and tech are available). This makes me wonder why not more people have requested this as a feature. It is not a new question, not at all, but obviously, it hasn’t produced much input into the suggestion option. I encourage everyone to voice the wishes there, as I mention it here very often.
https://www.maxon.net/en/support-center
To compare apps which each other is something I will not do here.
Cheers