I recently looked into ways to monitor my solar panels and my home's power usage, so I've got some experience with this.
Can you get the parts to do this? Absolutely.
Here in the UK, our breakers are in a 'consumer unit' with the breakers mounted on DIN rail - and the suppliers of industrial parts can supply DIN-rail-mounted power meters - such as this DIN-rail-mounted digital power meter:
However, I opted not to do this because in my country, any modifications to the consumer unit have to be signed off by a qualified electrician, due to a spate of fires caused by incompetent electrical installations. As putting an industrial power meter into a residential installation would be an unusual thing to do, I felt it would be challenging to find someone inclined to be adventurous in what they sign off.
I also had access to some other options - such as a wireless home energy monitor:-
I know you say you don't want to hang a clamp off the wires, but this was the option I went for, as it was a heck of a lot cheaper than getting someone to sign off something fancier. And being wireless, you can watch the readings from elsewhere in your home - in my case, I connected the receiver to a computer to record my power usage. However, I remain sceptical about magnetic clamps as a means of sensing, having seen it give nonzero readings before I'd even put the wire into the clamp.
My country also has smart meters with in-home displays - made mandatory by the government, and installed at the power company's expense. So it could be worth checking if your country has a similar scheme. Unfortunately, the smart meter supplied by my power company was pretty useless, which is why I ended up with the current clamps I mention above. Here's a picture of some similar to the ones they supplied me with:
Finally, many electricity meters in my country have an an LED that flashes at a rate proportional to energy usage - you can buy an optical pickup that will couple onto those. Unfortunately this didn't meed my needs for solar energy monitoring, as a single LED couldn't give info about electricity import and export at once - but it might work in your case, and they avoid both current clamps and the need to rewire your breaker panel.