I cut my DC/DC switching converter "teeth" on the ST Micro L5970D many years back based on designs I inherited from a colleague. Apart from getting some sensible compensation component values, they were very easy to use, and there were some higher current variants (L5972/5973).
Since then I have dabbled with some TI TPS series parts (e.g. TPS54622, TPS54561, TPS562200) but I was finding that some were really not that robust. I don't recall exactly which ones caused me grief (it was maybe 5 years ago), but I believe it was a lower current part so probably TPS56 something. Since I switched to some different TI parts (LMR series) I have had no further issues, so I've just stuck with them. I'm not saying The TPS56 series parts are inherently problematic, but I had a bad experience and tend to stay away from them.
These days I am doing a lot of mixed mains/battery power designs where the currents are not very high but are quite variable, so I mostly use something like the LMR14006/010, or for a little more current the LMR51420/30. There are a bunch of footprint compatible parts from TI, Richtek, and others vendors. The newer parts are synchronous and don't need a flyback diode, but if I have space I leave the diode footprint in case I swap parts for later BOM cost savings or due to part shortages. The final choice of which one to use will depend on your various constraints of board space, input voltage, output current, and quiescent current, but as long as you have a sensible PCB layout you can swap between a bunch these parts and mainly just need to review the inductor sizing, required capacitance, and feedback resistors (some have different reference voltages).
I also do the occasional design where I know there will only be a handful made, and in those cases I might just drop in a Recom (XP Power/Traco/etc) "7805 replacement" style module.
Anyway there are a ton of devices available. I almost always have a look in TI Webench for recommendations and simulations, but unless there is specific reason to change I stick with what I know and stock. It sounds like you are on the right track by using Webench and being open to ask others for suggestions.