I like to use all / more of them and combine the information. I work in an academic synthetic lab doing custom radiolabeling for our institute and others so we commonly move from one project to another and while we are at an acadmic institution our work is more like in a CRO so keep that in mind because other perspective might be different. Also I think you summarized the differences/advantages it really well.
TLC is quick, simple and cheap. No reason not to run it because you at least see if your starting material is consumed and new compounds are formed. By use of various TLC stains you can somehow identify your spots. I could run radio-TLC as well when doing labeling but we tent to not to because of the associated dangers. We prefer to run radio-HPLC because you dont end up with capillary filled with radioactive solution and you can use the vial for HPLC-MS or do scintilation counting.
Because of various works we do we have maybe 20 different LC columns from C4 through C8, phenylhexyl, multiple C18 to hilic therefore HPLC method developement is simple. ALso, each one of my colleagues and me have preffered go-to column when starting new method. Im pretty sure we could run most of our samples on C18 or the phenylhexyl (my fav

) and the peptides on C4 or C8. We dont have UPLC therefore our runs are like 60 minuets therefore we always do TLC first if possible.
GCMS is for the stuff thats not suitable for LC: to name a few we did: small aliphatic amines, silyl ethers, benzyl chlorides, ant pheromones.
We dont do calibration curves since we are not an analytical lab but we also developed an analytical method for separation and quantitaion of adenosine phosphates but thats not common. We just integrate the peaks to get rough idea how much stuff is there but if its 60 or 80% is usually not much difference.
I spent some very short time in industry RnD as well. We had an analytical department that developed methods for projects They had maybe 5 GC and LC systems. I just prepared the sample based on the method - much more rigorous that I dn at my job (=take small aliquot of reaction into ACN/water and dump it into LCMS) - but we got detailed analytical data esp. quantitation of products in the reaction. THe disadvantage was that it took significant time because they were quuite busy therefore I submit sample after 60 minutes of reaction which then asks to either add reagent or quench based on the results but I get results the next day...
TLDR: It all depends on various details but: TLC always then LCMS or GCMS. You can run 90% of analysis on universal column using maybe 3 universal gradients (slow, normal, fast). Develop specific method based on your needs and situation (developing method for a day if you have 1 LCMS in lab for 20 ppl wont make you any friends)