As a practical matter, I change the composition for the following reasons:
Save time in the purification. A gradient tends to reduce resolution compared to isocratic (later eluting peaks come earlier).
I have early eluting peaks where I need more resolution, so I may have a gradient segment where it is isocratic or changing slowly to resolve those compounds.
If I am not getting the selectivity I need, I'll change the solvent (change methanol for acetonitrile or THF, if running C18, for example).
Improving the loading capacity for the desired compound (matters more in preparative chromatography than analytical
I tend to think in terms of preparative work, so time and purity are important for me. For analytical work I would worry about time, resolution, and reproducibility being important.