One of the (many) benefits of having an always ready sauna stove is the temperature of the bench and the walls when you enter. At first it felt weird when sitting down in the sauna, but now that it's been almost a year I'm finally starting to get used to it after being used to sit down carefully not to "burn" yourself on the hot bench or walls.
In the traditionally heated sauna everything will get hot while heating it. Of course the wood doesn't get dangerously hot, but it still feels uncomfortable when you first touch it. Or if they are not enough then the sauna itself probably isn't hot enough yet.
The always-on stove keeps the sauna a bit warmer than normal room temperature. The insulation isn't perfect. When there is no need to preheat the sauna everything is cool when entering. But as soon as you throw the first scoop of water at the rocks things heat up pretty fast. At that point it doesn't matter anymore as you are also warming up at the same rate so the issue in the traditional sauna with the big temperature difference is absent.