fracture mechanics parameters in ASTM codes (E399 E1820 E647) are not derived from empirical relations but from FEM! They are based on linear elastic fracture mechanics! Even the crack tip stresses/strains are derived from solid mechanics (Williams series).

I suggest this text:

https://www.researchgate.net/publication/316927229_Computational_fracture_mechanics

Technical Report Computational fracture mechanics

The subject is still important, because you would need some sort of analytical validations for your analysis, as a benchmark.

RE:  "..FEM is showing the stresses around the crack tip? "

Yes and no.  The critical things are happening AT the crack tip (a.k.a., 'singularity'), so stress-based calculation become untenable.  Refine the mesh as much as you want, and the stresses will never converge there.   

The only way to gauge the possibility of failure becomes fracture mechanics.  It's the stresses AROUND the crack in some FE codes that can then be used by special FE tools to analyze fracture mechanics parameters. 

I'd agree with Gopala too that you need ways to validate your analysis.  Or if you can't validate a complex model, you should at least be able to create a simple model (e.g., plate with a central crack) and validate that against a LEFM closed-form solution. 

yes, it is the most useful one. Recently Ranjbaran &Ranjbaran and their research team proposed the so called "state based philosophy (SBP)" where every phenomenon may be treated based on exact reasoning and mathematical logic. The SBP applied to the fracture mechanics and all parameters of fracture mechanics are explicitly and exactly determined. The new fracture mechanics, is in close agreement with the test results. It is different from the classical fracture mechanics (empirical and/or finite element based) in the sens that it is based on exact mathematical logic. Therefore all ambiguities in the classical fracture mechanics (singularity, the unknown domain of crack effect, the strain released energy, ant etc.) are no longer present. The new fracture mechanics led us to solve other damage problems, e.g. buckling, yielding, and etc., with the same concept.

Fracture mechanics is based  mostly in elasticity and elasto-plasticity models from mechanics of solids. The FE tools used nowadays take these models as the ideal reference. Empirical fromulae from laboratory and standards are useful for desing in engineering. These tools are always compared to the ideal reference models from Fracture mechanics. So, no, you cannot replace the ideal scientific base with the tools that ared used to precisely apply this science in engineering practice.

It is a good question. It actually depends on the FEM solution and assumptions.  For example if you use FEM based on elasticity then you will have stress singularity around the crack faces. But, if you use FEM coupled with more realistic assumption like plasticity or cohesive zone, then you probably get better results.

Classic Fracture Mechanics relations are used for quick calculation of fracture parameters for the simple geometry and loading pattern. Sometimes you do not want to spend a lot of time on generating mesh, processing and post processing to get the fracture properties....

We cannot replace fracture mechanics with FEM simulations. Both are important. The choice depends on the geometry, type of constitutive equations you are using (standard or proposing a new approach), depth of the analysis (I agree with Elyas Goli, sometimes a simpler approach with comparatively larger safety factor is preferred). Depending on the type of your study, you may apply both approaches at the same time for validation purpose.