User Uploading Proof Of Payments

I am building an online store and one of my requirements is a user being able to upload proof of payments for the admin to browse and download. I have had a look at some plugins but most of them seem to say file uploading might not work in older browsers or mobile browsers, which would be a huge problem for me.

My question to you, WordPress aficionados, is are file uploads really unstable in a large percent of browsers, meaning I should instead have the customers directly email their proof of payments instead ??

Any advice in this matter would be greatly appreciated 🙂