Yes, it can be frustrating to have all Amiga software downloadable from Internet, but only on PC.
When I had only A500 at my disposal, I used serial cable between PC and Amiga. I was lucky I had my old Amiga disks, so I had JRComm ( If I remember correctly) program to use Amiga side serial connection. But it was slow transferring bigger files. The bottom line is that you must obtain some hardware/or software for Amiga side in order to transfer software to Amiga.
For Amiga 1200 / A600 it's a lot easier because you can use CompactFlash card reader in Amigas PCMCIA port. That is how I'm dealing with transferring issues, and it's fast.