If you have a PSP Street then Sony gave you the proverbial middle finger since both Media Go (PC Software to download and manage digital PSP games), and transferring games from PS3 to PSP doesn't work.

But if you have a PSP that can connect to WiFi you absolutely can still download PSP games. You just need to

1. connect your PSP to WiFi a challenge in it of itself

2. generate a Password for your account since Sony requires 2fa and PSP doesn't support 2fa. Its on your Sony Account settings somewhere from a browser.

3. sign into your Sony account on your PSP

4. goto account management

5. select transaction management

6. select downloads list

7. select game you wanna download

Lots of guides out there for extracting PSP ISO or PS1 ISO from digital games on YouTube. Definitely worth looking into to preserve your collection