TL;DR: To be on the safe side, wear goggles.
Full story:
According to this post the laser power when the door of the enclosure is open is set to 0.5%. On first glance, that would be 50mW for the 10W laser and safe to look at. BUT. In order to assess the risk, you need to understand how laser power is controlled. It is not that the laser is really set to 50mW, but the method used is pulse width modulation (PWM). This means that the laser is switched on and off in rapid succession, depending on implementation a few ten to several thousand times per second. It is “switch on laser for time x, switch it off for time y, repeat.” The ratio between x/y determines the average power the laser emits. E.g. is the laser is switched on for 0.25 ms and switched off for 0.75 ms each cycle, the average power emitted would be 25%, i.e. 2.5 W. However, during the 0.25 ms switched on, the laser emits the full 10 W, in the 0.75 ms 0 W. If 0.25 ms of 10 W laser directly hitting your eye would be enough to create damage, then you should always wear goggles.
With Snapmaker 2.0, when I looked in the source code two years ago or so, the PWM frequency they used was ~100 Hz (pretty low). So 100 on/off cycles per second. One cycle would be 10 ms, with 0.5% duty cycle that would mean a 10 W laser pulse of 50 µs every 10 ms. Is this enough to damage your eye on a direct hit? Honestly, I don’t know, I guess with a bit of research you could find out.
Last thing that goes into the equation: Reflection. If the laser hits material that reflects the light diffusely, like e.g. white paper or wood, the 10W laser power are widely distributed and become harmless very quickly with distance. The danger comes in if you get a beam reflection, like e.g. from a mirror or a piece of metal (like the screws that hold down your laser platform). A direct beam hit to your eye is what is most dangerous, and my cause irrepairable damage within fractions of a second.
I personally can feel your pain handling work origin with goggles on. Also, the color scheme of the touchscreen is a bad choice with amber goggles, it is difficult to handle it with goggles on. So I personally do work origin without goggles IF I can be pretty sure that I’ll have no direct reflection, i.e. the material is not shiny/reflective like a mirror anywhere near the work origin AND there is basically no risk of accidentily moving off the material and hitting something metallic by a mistake press on the touch screen. But this is me taking the risk, I do NOT encourage you to follow my example. And: I am not an expert, just a lay man like you.
So again: long story short - wear goggles all the time the laser is on.