I forgot another important reason why Portland cement is preferred over lime these days. Lime takes a while to set (a few days?), cement sets faster.
Cement will still take many days to reach full cure time (measured in increasing PSI ratings)
https://www.ce.memphis.edu/1101/notes/concrete/section_3_pro...
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> Lime takes a while to set (a few days?)
Up to 30 days to set, and depending on the type of lime (hydraulic or non-hydraulic) and form/process (putty, hot mix, etc.) up to a year to reach full hardness.