The old-timey blade is called a straight razor. A safety razor is one of these

I use a safety razor because the replacement blades are cheap and I seem to get a much closer shave
You're not going to believe this.
Having advanced a long time ago to state-of-the-art shaving and finding it irksome, I some years ago began reverting, stepping backwards to ever-increasing primitive means of shaving, hoping that some more-ancient instrument might be more useful.
What you call "safety razors"--my father used them himself--apparently are not on the market in all of northeastern Nebraska, even though dozens and scores of other models are. Not even at Wal-Mart. This is a trade area about as big as New England minus Maine all put together, with a whopping 50,000 inhabitants, and so it seems there
should be a market for that.
But no. I dunno what the safety razor people have against us. And yeah, I know I could probably get the things on-line, but basically I'm lazy and prefer just to take what's on a shelf.