As a developer of a similar vintage, I can relate to this mindset, but I think we should be careful about it. We learned in an era when differences in browser behaviour were a big deal and new versions of browsers sometimes came along years apart. But those days are long gone — even Safari now gets several updates each year — and we should let the habits they created go with them.
Should we be cautious about relying on non-standard features or trusting the perma-beta culture that Google never seems to have grown out of? Of course. But there have been many recent developments that are useful and already widely supported, and not using those when they provide a good solution to an immediate problem seems counterproductive.