Graphs should have a purpose and communicate information as clearly as possible. Scales and units should be chosen to most effectively convey information. Logarithmic scales are a poor choice for the information being displayed.
For a given set of parameters (of measures such as social distancing, mask wearing, weather, etc.) new infections will not rise by some specific, absolute number. Rather, similar environments result in similar rates of new infections as a percentage of existing, active infections.
Again graphs should serve one purpose. The purpose of those graphs is clearly, by the axis labels, supposed to display continuous deaths over a set period of time.
The linearly scaled graph displays this clearly, the logarithmic one does not. If the x-axis displayed into some future time, yes I'd agree a logarithmic scale may be more appropriate. But that would be displaying a graph of predictions at that point, which is something totally different than the two example graphs are showing.