Difference between using a first order low pass filter and a second order
It depends on your spec for harmonic distortion or SNR ratio with the harmonics being noise.  It also depends on your group delay stability on the fundamental if DC phase stability matters.

Comparing the fundamental as a signal only and the rest as noise;

A square wave has a SNR of about 8dB.

A triangle wave has a SNR of about 16dB.

A 1st order LPF drops -3dB if the breakpoint is at the fundamental  then -12dB per successive odd harmonic thus a gain in SNR of about 8dB to 9dB
harmonic.  

A 2nd order LPT doubles the above SNR improvement to 16~18dB
A 3rd order LPT triples to 24~27dB
A 4th order LPT quadruples to 32 ~36 dB improvement on the original 16dB triangle.

Whereas a -40dB 2nd order notch filter can do even better on 3f with the 2x-LPF and a recursive notch filter even better.


  why wouldn't I use a first order low pass filter ?


It depends on your spec for sine spectral purity in dB ( 40dB ok ? or 50 or 60dB? )