Hopefully, you have a monorepo or something with similar effects, and a lack of fiefdoms. In that case, if the current way is undocumented and/or inconsistent, you make it better before or while adding in your new approach. If there are 4 ways to do the same thing and you really want to do it a different way, then replace one of those ways with your new one in the process of adding it. For extra credit, get to the point where you understand why you can't replace the other 3. (Or if you can, do it! Preferably in followups, to avoid bundling too much risk at once.)
A lot of inconsistency is the result of unwillingness to fix other people's stuff. If your way is better, trust people to see it when applied to their own code. They probably have similar grievances, but it has never been a priority to fix. If you're willing to spend the time and energy, there's a good chance they'll be willing to accept the results even if it does cause some churn and require new learning.
(Source: I have worked on Firefox for a decade now, which fits the criteria in the article, and sweeping changes that affect the entire codebase are relatively common. People here are more likely to encourage such thinking than to shoot it down because it is new or different than the status quo. You just can't be an ass about it and ignore legitimate objections. It is still a giant legacy codebase with ancient warts, but I mostly see technical or logistical obstacles to cleaning things up, not political ones.)
A lot of inconsistency is the result of unwillingness to fix other people's stuff. If your way is better, trust people to see it when applied to their own code. They probably have similar grievances, but it has never been a priority to fix. If you're willing to spend the time and energy, there's a good chance they'll be willing to accept the results even if it does cause some churn and require new learning.
(Source: I have worked on Firefox for a decade now, which fits the criteria in the article, and sweeping changes that affect the entire codebase are relatively common. People here are more likely to encourage such thinking than to shoot it down because it is new or different than the status quo. You just can't be an ass about it and ignore legitimate objections. It is still a giant legacy codebase with ancient warts, but I mostly see technical or logistical obstacles to cleaning things up, not political ones.)