Try installing LTspice XVII. Just dl the .exe installer ( https://ltspice.analog.com/software/LTspiceIV.exe IIRC that's for WinXP...
Thank you, this one worked out of the box

[ The one that failed was an MSI installer. ]
Maybe not only Phase, but Amplitude, and PSR and CMR, maybe even Distortion 
I wonder how well large signal distortion is modeled. Can it be trusted?
I tried high resolution transient analysis with a 10Vp sine wave and LT1002.
At 100 Hz, THD is virtually zero for both simple and nested followers. The nested follower is superior in terms of gain magnitude error (large signal RMS value obtained through transient analysis).
From SPICE log:
simple: Total Harmonic Distortion: 0.000001%(0.000000%)
nested: Total Harmonic Distortion: 0.000000%(0.000000%)
rms1: RMS(v(vout1))=7.07105828433 FROM 0 TO 0.05
rms2: RMS(v(vout2))=7.07106836523 FROM 0 TO 0.05
gain_err1: rms1*sqrt(2)/10-1=-1.3473966517e-006 <-- simple
gain_err2: rms2*sqrt(2)/10-1=7.82577911362e-008 <-- nested
At 1000 Hz, the nested follower has the better THD (although both are still very low), but the simple follower now wins in terms of gain magnitude error (large signal RMS value obtained through transient analysis).
simple: Total Harmonic Distortion: 0.000648%(0.000000%)
nested: Total Harmonic Distortion: 0.000017%(0.000000%)
rms1: RMS(v(vout1))=7.0710613613 FROM 0 TO 0.005
rms2: RMS(v(vout2))=7.07113146388 FROM 0 TO 0.005
gain_err1: rms1*sqrt(2)/10-1=-9.12247829277e-007 <-- simple
gain_err2: rms2*sqrt(2)/10-1=9.00175430596e-006 <-- nested
EDIT: Added FFT plots for transient analysis, 1kHz.