Because it could end up with the government blocking access to websites critical of it, or going after individuals accessing such websites as they will now have all "proof" they'd need for that.
In an extreme case, they could potentially blacklist your ID to prevent you from spreading "harmful" political opinions, cutting you off the web entirely.
The OSA doesn’t make any provision for the government blocking access to websites that are critical of it. This is a pretty long slippery slope that you’re talking about, where the government directly enforces the rules instead of OFCOM, and the rules are substantially different from those currently in force. In other words, you are basically just saying that “things might get worse”. This is true, but it’s not really a very strong criticism of the OSA (which I do not support).
Also, any hypothetical attempt to abuse the OSA to rein in political dissent would almost certainly be subject to legal challenges under the ECHR.
In an extreme case, they could potentially blacklist your ID to prevent you from spreading "harmful" political opinions, cutting you off the web entirely.