Earlier quoted context omitted.
On a positive note, it sounds like proprosals to use newer technology are welcome. I keep seeing the opposite, "No this is too different, could break stuff."
If it ain't broken, why fix it?
Sometimes it can make you more productive. Or though your site is still responding to current customer demands in a timely fashion, you know that the mobile experience could be significantly improved now that browsing via cell phone is on the rise.
Another thing to consider is employability both from a company and individual perspective. If you can keep up with moderately current (not the latest and greatest) trends, you'll attract people who want to grow in their careers. I wouldn't want to work on C# 2.0 using Visual Source Safe. It's hard to convince a company that you can learn git on the job.
In general I like to move without introducing breaking changes. I'm not a cowboy coder, it's really exhausting working with one. I do think there's merit in realizing when it's time to change though.