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The left side replaces your diodes or zener with an active BJT that measures the current in \$R_\text{ISET}\$ and makes adjustments the base voltage of \$Q_1\$. This is much better because it also takes into account \$Q_1\$'s Early Effect by measuring it, too, and correcting for it. So this is a big improvement in that sense. However, it remains sensitive to \$Q_2\$'s temperature and part variations. It also is sensitive to the supply voltage because that can greatly increase the current in \$R_1\$ and thereby require higher collector currents in \$Q_2\$ which affects the base-emitter voltage and thereby also the collector current of \$Q_1\$. So it will still respond somewhat to wide swings in the supply voltage, causing load current variation with supply voltage. It's just a bit better on a few scores. And it can be better designed/managed, if you put some work into it.

Another approach used by many is to just perform lots of Spice runs (or use lots of Excel runs) to achieve similar results.

The left side replaces your diodes or zener with an active BJT that measures the current in \$R_\text{ISET}\$ and makes adjustments to the base voltage of \$Q_1\$. This is much better because it also takes into account \$Q_1\$'s Early Effect by measuring it, too, and correcting for it. So this is a big improvement in that sense. However, it remains sensitive to \$Q_2\$'s temperature and part variations. It also is sensitive to the supply voltage because that can greatly increase the current in \$R_1\$ and thereby require higher collector currents in \$Q_2\$ which affects the base-emitter voltage and thereby also the collector current of \$Q_1\$. So it will still respond somewhat to wide swings in the supply voltage, causing load current variation with supply voltage. It's just a bit better on a few scores. And it can be better designed/managed, if you put some work into it.

Another approach used by many is to just perform lots of Spice runs (or use lots of Excel runs) to achieve similar results.

Note: Pete W mentioned in a comment below that the LM4041 is a high-side device similar to the TLV431 device. I hadn't known about it and now I'm glad to hear of it. So I'm making a note about it within the answer to capture the option. Sometimes, you want a controllable high-side source rather than a sink, depending on load requirements. So that's a nice catch from Pete W. Thanks!

Another approach used by many is to just perform lots of Spice runs (or use lots of Excel runs) to achieve similar results.

Summary

Sensitivity equations are also very, very useful in helping to both quantitatively estimate how a variation of an input parameter impacts a design goal's output parameter. The process allows you to first find out which is of more concern and then also if that concern is sufficient to warrant more design effort. Or, alternately, to realize that that the design goals have been met and the design can be considered complete.