I promise that readers will recognize a plot even without lines around it.
I'm not so sure. Without lines or tick marks, it's not all that clear what the squiggly line is. I'm sure some squiggly lines would be more obvious, and a scatter plot without axis lines or ticks would be more obvious still.
Suppose your data is how the GDP of some country changed over time, so the x-axis is years and the y-axis is GDP.
When you introduce tick marks and tick labels, I think you've already done most (if not all) of the work that the axis lines do. Now it's way more clear what we're looking at, and to the extent that the reader is invited to make ratio- or interval-level comparisons, the tick marks and labels provide most (all?) of the relevant information.
I'm not so sure. Without lines or tick marks, it's not all that clear what the squiggly line is. I'm sure some squiggly lines would be more obvious, and a scatter plot without axis lines or ticks would be more obvious still.
When you introduce tick marks and tick labels, I think you've already done most (if not all) of the work that the axis lines do. Now it's way more clear what we're looking at, and to the extent that the reader is invited to make ratio- or interval-level comparisons, the tick marks and labels provide most (all?) of the relevant information.