The role of fact checking is not to strive for partisan balance but rather to identify public comments that are untrue.
American conservatives would fall afoul of fact checking far less frequently if the conservative worldview wasn't wedded to talking points that are not factually accurate. For example:
There is no evidence of widespread voter fraud in the 2020 presidential election. There is no evidence of ongoing large-scale voter fraud in US elections. There is no evidence that the incoming Biden administration intends to end capitalism. There were no 'convoys' of migrants preparing to violently storm the US-Mexico border prior to the 2018 midterms. Barrack Obama was not ineligible to serve as President. There is no evidence that the Democratic party is detaining children in the basement of a pizza parlor. There is no evidence that the Democratic party is run by a cabal of pedophile cannibals. Etc.
A fact checker who does not point out the fact-free basis of these, and other, deeply-held conservative talking points is simply not doing his/her job.
If the weight of fact checking falls primarily against conservatives, then conservatives can fix that problem by lying less frequently.
You're down voted, but this is no joke. Social programs are very often hyper-pragmatic, overly specific bandaids that effectively pile on each other indefinitely. Cutting social programs essentially only reliably occurs at bankruptcy or collapse, it will almost never occur as the result of the democratic process.
People do not run successful campaigns on the basis of displacing hundreds of San Francisco families, for example, regardless of whether or not those families are rightfully entitled to their housing or not. Once people have come to rely on something, it will upend their livelihood to remove it, and that is not something most people are comfortable voting for.
If you've ever worked in a government job, you can compare the state of the bureaucracy now to previous versions of the texts, and see that they only ever grow and compound on themselves.