It seems that there are mayor softwares around offering a multicurve framework based on bootstrap. I find this puzzling nowadays, given the distinct advantages of best-fit optimization methods and the hurdles in extending bootstrap techniques to the multicurve setting (e.g. cyclic interdependencies among curves, nontrivial products, usage of nonliquid instruments, overall coherence, dates mismatches, TOY effect, pre-first-tenor forwards, joint curves+term structure dynamics calibration etc). Therefore I must be missing some major drawback of full calibration or overestimating issues for bootstrap. The literature is outdated and mostly partisan, just like those I asked to dismiss either choice altogether. Could someone please shed some more light on these two possibilities and respective drawbacks?
(Moreover, Henrard mantains that for best-fit calibration a Newton-Rhapson optimizer suffices, while in my opinion the landscape is not so well-behaved... any views on this?)