I tried to make that distinction clear. I'll see if I can do a better job.
Most companies ask a customer for a telephone number in their forms and in their applications. Actually, just about any context where the customer's mobile device is not the item of attention. This was my first encounter with a company that specifically requested a mobile telephone number in their application. This unusually specific request illuminated some interesting possibilities in my mind.
If you experience circa 2014 has been different, actually, that's great! I'd like to see and compare some similar event applications around that same time period. (Still, it was the possibilities for the uses of a mobile number that really flagged my interest as well as the relevance to this conversation, not the rarity today of companies specifically requesting a mobile number.)
Did they use those exact words? Sounds strange to me as most American English speakers would say “phone number” or “cell phone number”, and both are used pretty much synonymously (because in practice they basically are) for a long time. More formal forms (government forms) might ask for something like “daytime phone number”. In particular I haven’t seen the word “telephone” in ages.
I'd have to unearth the screenshot I took some years back, but that strays from the point, doesn't it?
They weren't asking for home number, work number, and mobile number. Or as you mentioned: daytime number, evening number. It was more along the lines of: Name, Address, Mobile Number, Company Name, Job Title, etc. They specifically wanted a mobile number and no other type of number.
Were they wanting a mobile number so they could more easily research an applicant using their internal tools? Only they would know. But it drew my attention to the possibilities and the importance of obtaining a mobile number.
Back to OP's question, part of the reason a mobile number is required to create a Facebook account may be to help tie different types of records together. Of course, as mentioned, there are other reasons, such as security. Users will understand and provide a mobile number for that reason alone.
