First of all, the device is not a PRNG. All cryptographic functions remain securely within the chip on the card. The device is little more than a user interface. Because it's air-gapped from your browser, it can't be "hacked" by a web page or malware infected computer. And because it's your from your bank, you can trust that it's not a PIN-skimmer keypad. These are very good security attributes that make these devices powerful tools against fraud.
You enter the PIN in the device, which then sends the PIN to your card, and the card verifies it according to the ISO/IEC 7816-4 spec. The card returns only the results of the PIN verification attempt to the reader, which it then displays to you as either an 8 digit authorization code, or as an invalid PIN error. Three consecutive failed PIN verification attempts result in a card that must be reset at an ATM authorized by your bank.
As you noted, this is a tragic weakness in the protocol, but for a completely different reason than cryptography. A mugger can strike you in a private place, and demand your card and your PIN, and he can use your PINSentry on the spot to prove you're not lying. It used to be a mugger would have to drag you to the bank to verify your PIN and risk the security cameras, but now they can do it in the convenience of a dark alley. At least three murders have been committed by robbers gathering PINs.
To be more secure for the user, the device should continue merrily on its way regardless of the validity of your PIN, because the bank should be validating the PIN later on. The problem is this was all designed and decided when many small merchants were still authorizing cards offline. With almost 100% ubiquity of the Internet across the populated areas of our planet, I see little reason to continue accepting offline payments.
As far as PIN security on the chip, that's a lot stronger than the typical mugger. The chip is engineered so that it's very difficult to access the memory on it. It's not like a flash drive or old-school payphone chip, where it's simply a storage device. It's a cryptographic processor, with algorithms and keys and certificates loaded into the silicon only after verifying the signatures on the data. You can't issue a command like "set counter memory location 1234 = 0". Instead, the command to reset the PIN is part of an HMAC protocol, with cryptographic authentication that must be generated by the bank, and the MAC is verified on the chip before it will actually reset the PIN counter.
The chips are reasonably well-protected against tampering, considering they have to cost only a few pennies each. Focused ion beam microscopes have been used to read bits from the cards in the laboratory. Timing attacks have been reduced by improving the designs of the encryption algorithms. As far as I know, differential power analysis attacks can still work, but some chip designs can even withstand those.