For a linear PSU I would really recommend not using the negative-bias trick to try to get 0 V from a 3-terminal regulator. As per this question stability of the negative rail directly affects output stability.
Linear regulators are simple enough to make building them with an op-amp no problem (in which case as @Michal observes you can get as close as the op-amp will get you if you don't use a negative supply). But a negative supply is quite easy if you are using a transformer: just capacitively couple a second bridge rectifier and rectify and connect to the main bridge rectifier backwards. Then, since your main op amp will never put much load on the negative supply (only needing to go down to zero), and likely has a good PSRR, you can effectively* ignore the stability of the negative supply and focus on the positive. Something like this design which is to be found all over the internet but is discussed very well on that page.
Regardless of what you build, do read that linked article: there are some very good practical points on building a PSU you can actually use and maintain.
Lastly, as noted in the linked article, you do need to go down to 0 V (ish). You want to be able to apply current slowly to something you have built, so you can spot that backwards-connected IC whose protection diode is causing surprising current consumption but which will survive if you turn it off now. Before I built a 0-30 V supply I blew a lot of ICs wondering what was happening. Likewise you do want current limitation.
*for the kind of regulation most of us actually need.