No you don't. Not as a sticky mushy human with emotions watching tokens drip in. There's a lot of feeling and emotion not backed by hard facts and data going around, and most people would rather see something happening even if it takes longer overall. Hence spinner.gif, that doesn't actually remotely do a damned thing, but it gives users reassurance that they're waiting for something good. So human psychology makes time to first token an important metric to look at, although it's not the only one.

Some kinds of spinners serve as a coal-mine canary indicating if the app has gotten wedged. Not hugely useful, but also not entirely useless.