New methods can open up new possibilities for answering certain research questions or, at least, they should offer some sort of significant technical improvements. So I guess it totaly depends on what you want to achieve with your experiment in order to evaluate whether a more modern method can be replaced by a (supposedly cheaper, but perhaps more labour intensive) older one. For instance, when it comes to qRT-PCRs many researchers are opting for pre-mixed everything (even primers) rather than designing own master mixes which are much much more cheaper. Granted, when purchasing ready-to-use chemicals you can mostly be certain of getting a high quality product. Everyone needs to weigh the pros and cons for their invidual situation, most of the times it comes down to budget.

I nominate DNA methylation clocks to measure aging. The problem is not that it's expensive, but that they don't work in the context of intervention. People need to double-check on whatever their methylation clock is saying with a good old life span study. But nobody has time for that anymore, and if they did it, they wouldn't like the result. Instead, they just take the clock on faith.

This question makes me laugh. You can do great research with older techniques. I worked in a lab that was using paper chromatography and thin layer chromatography that published a bunch of papers. Go for it.

I say the question makes me laugh because I understand. I have seen many times that people jump on a new technology and it becomes a fad.