> But I was curious if there is working happening on L1 defence — fixing the enzyme that fixes the wrong copy paste mechanism. Or making the enzyme get more efficient and powerful. Is that line of thought even valid?

Mutations in general are not the defining quality of cancer. It's mutations in these very L1 safeguards. There are several such safeguards and a cell needs several mutations in those to become malignant. Eg. https://en.wikipedia.org/wiki/P53

Correcting genes only works in certain conditions (e.g. limited single strand breaks), in a narrow time frame during cell division, safeguards rather trigger cell suicide, or if that fails they mark the cell for destruction by immune cells. A cell can't fix DNA which made it through cell division once, because it got nothing to proof-read against.

After the safeguards are gone, everything goes and genetic diversity increases quickly within each tumor. This diversity is what's making cancer treatment hard. At some point there won't be a shared vulnerability in all malignant cells. The repair mechanisms are working in favor of the cancer now. For example, with radiation therapy you preferably want to induce DNA double strand breaks, because cancer cells can't repair those. Otherwise you need to increase the radical burden enough to overwhelm repair, but migrating radicals may damage distant cells, too.

I presume you could hypothetically inject mRNA of a working safeguard gene (eg. P53) into all cells (at some point cancer cells can't be selected exclusively, since they lost identifying marks and present as stem cells), so the functional enzyme or transcription factor is forced to be built inside. I am sure people are trying this right now. However, the inner workings of cells on a molecular level are insanely complex and our understanding is only scratching the surface. As with P53, you have a transcription factor, which means it's modifying gene expressions elsewhere. It's only a small part of a complex regulatory cascade. I doubt there is a safeguard target, which can easily be injected without considering the precise timing and environment within that safeguard cascade in the cell. Of course, the rest of the safeguard system needs to be present in the cell to begin with. Mind you, you don't want to cause cell suicide in healthy cells, so you want to restore the function of whole selective complex.

Then there is the question of delivery. Can you deliver eg. the mRNA to every cell without raising suspicion of the immune system? With the COVID vaccine, the enabling breakthrough was the delivery vehicle, not as much the mRNA part. Can you even reach the cancer cells at all? Cancer cells are frequently cloaked, shadowed or cut of by senescent, or necrotic cells, or acquired unique ways of metabolic adaptations. A bit similar to bacterial persistence, like M. tuberculosis, which can evade bodily and chemical defenses for decades.

The take-away: Life is complex beyond comprehension! Despite simplifications taught in schools and reductionist zeitgeist, we actually know very, very little about what's going on in genetics and molecular biology, most medical knowledge is empiric guessing instead of explanatory understanding.