I use FEA and computer software for every slab I design. The pressure of today’s design office and the increasing complexity of structural arrangements make hand calculations mostly redundant and I find that generally the code is not directly applicable. For nice rectangular grids with equal spans and uniform loadings the codes are fantastic, and these assumptions of "equal spans and uniform loadings" are regularly stated throughout. This does not tend to happen in the jobs I do; irregular grids, opes everywhere, irregular loadings, steps, recesses, transfer columns off grid, triangular and circular floor plates etc. The numerous assumptions made to fit the design of the building around the code is putting the cart before the horse and generally results in an over-designed structure. While I realise the code can't cover every scenario, it should be more applicable to modern day FEA.
Sure there are some people do not understand FEA and believe the software will do the work for them. Part of the problem lies in the understanding of FEA. I spent 4 years solving matrices and learning the many different methods of structural analysis. Good fun at the time, but of limited use in any of the modern day design offices I have worked in. Building character and rigour was probably the intended end product. Part of the problem is that it requires effort and time understand structural analysis. These same people would have struggled with stiffness or moment redistribution methods in the days when these were cutting edge techniques. The profession, as any other, will always have lightweights.
I currently design both PT and RC slabs. I have done PT calculations by hand and enjoyed doing it. There is no doubt you get a better feel for what you are designing, although this is probably because you have sent an hour looking at it. PT design is not a quick process. Add to the equation the client who changes his mind like the weather and FEA is the only option. In my opinion FEA is not the future, it is the now. It is time the codes and universities we work to and attend recognise this fact.