This is relevant to the Kuhn - Popper debate about the way science works, and there is a considerable literature here... I don't know about statistics, but I do know this is extremely common! A new simpler approach will usually be dismissed out of hand with scant regard by the powers that be with their strong ties to the traditional model.
Kuhn notes that researchers get locked into Paradigms. Those in positions of power (referees and editors, professors and deans) prefer papers that continue their work, use the tools they invented or are familiar with, cite their journals or journals indexed by their favourite citation company. There is also a factor of workload in relation to interest: They skim things quickly and pay particular attention to headings, tables, figures, equations and references - looking for things that connect to them/their interests/their journal. Some reviewers show no evidence of having actually read the paper, particularly for so-called 'top journals'. If they are not interested, or they have decided it a 'poor approach' a priori, then it doesn't matter how good the approach is or the results are, and you will be flipped off with comments about the style, format, equations or references (e.g. a complaint of lack of references to X or insufficient or unnumbered equations, or lack of road map glue telling them there is are Introduction, Methods, Results and Conclusion sections). That is there are not only paradigms within fields, in relation to how you tackle a problem, or the theoretical framework or model you work in, there are paradigms in relation to modes of presentation.
Popper on the other hand espouses Parsimony and Refutation. The simpler theory or model is better, other things being equal. A poor theory grows more complex as it keeps being adjusted or extended to deal with new cases that cause it difficulties. Usually the poor theories and models don't die off until their proponents and perpetrators do, until they get so complex as to be completely unmanageable and they eventually topple over and fall into oblivion. Conversely, a simple model will be ignored until it is demonstrated that it handles everything that the older theories tried to do, and makes new advances and predictions that are borne out. Popper's ideal researcher is totally different from Kuhn's dogmatic paradigmatic researcher. A good researcher is making predictions into the unknown where the different theories predict different outcomes. A good researcher is not trying to bolster their models, but rather to refute them - find the holes rather than plug the holes.
So how do you deal with this? A very good question - glad you asked...
You have to face it head on. Choose publication venues that are high quality but have the kind of format and expectations that allow you to present your new simpler ideas and models, even though it may not be fully worked out and compared against all your thousands of competitors and their thousands of datasets or examples. Get feedback, and find who is sympathetic, where they publish/review/edit etc. Eventually, you need to target the archival traditional journals, the bastion of the current paradigm, and fit things into their mould, follow their rules, explain the equations/models you are competing against in detail, especially those that are pushed by the journal and its editors/authors (at least they get a citation). Clearly point out the advantages...
- The theory explains more with less (effectiveness/parsimony)
- The model/algorithm is shorter and/or runs faster (efficiency)
- The results are more accurate and/or have lower variance (efficacy)