My employer does not accept emailed receipts/bills, which can be troublesome.
That is troublesome, but the overall trend is only going one way, and that's toward email receipts. Eventually your employer will have to accept them.
You have a staffing shortage because you don't pay your staff enough money. Raise their wages and you will attract more than enough people to any job you have on offer.
That might result in the hotel having to raise their room rates and then customers preferring competition who haven't raised theirs. Depends on margins and supply/demand, like everything.
I must say, the only calls I have received on my hotel landline in recent years have been from either hotel staff, or a colleague calling to say he/she would meet me in the lobby. Everything else is mobile phones or instant messaging/Skype.