I would probably disagree about the necessity to include PCR conditions these days. It is historically true, that all the primers, the PCR mix and machine (programe) have some kind of influence over success of PCR. So to be absolutely exact, you would need to specify all of this.
But then what, using different polymerase/mix if it's not just some general Taq (and the authors are not using general Taq possibly anyway) and having a different cycler (I have seen complete protocols listed, almost never the cycler in classic PCR) will cause you to change the conditions, since you cannot simply duplicate them.
This is still something you need to do and chceck (specifity etc.) on your own.
However now, with PCR mixex that are able to work accross range of temperature, that are optimized for specificity, these detailed conditions lose point. I got into this problem, when we were supposed to make a method section to a book, using primes from different labs, I was putting them together for other labs that wan't to sequence those genes. But I wondered how meaningful is actually to put detailed conditions everywhere if everyone uses different mix? You either have a "good" mix, that will with a decent primer pair work generaly over a large set of conditions, or you have a mix/polymerase that needs a lots of optimizing.
Detailed conditions wouldn't help you in either case.
So at the end I only divided the amplicons on "easy" and "difficult" amplification, and put there some rough Tms of the primers and amplicon lengths. For those difficult templates I tried to assess the reason for dificultness (high/low GC, ....) and some recommmended PCR aditives. It would be pointless to list all the different protocols.
Today many mixes may be hotstart with different conditions, of specilized polymerases also with different conditions.. you always need to use basic info (Tm from a calculator you are used to, some companies have their own, amplicon length) and use it in accordance with your polymerase recommended protocol.
(for Phusion I would add, that is more sensitive to right Tm than other polymerase I use (QIAGEN HotSTarTaq) and also, NEB has it's own Tm calculator for Phusion, that often calculate different Tm, then primer3 for example, but their works better for Phusion, of course)