Speed up nonsparse AD initial setup significantly

We have been setting `ADReal::do_derivatives=true` by default and only
toggling to `false` during residual computation. This can be very bad
for non-sparse calculations. For instance in a navier-stokes input file
supplied by Gavin Ridley, I saw 10 seconds spent in initial condition
computation and 9 seconds in `ComputeMaterialsObjectThread` for a total
of 19 seconds in `FEProblemBase::initialSetup`. This was 27% of the
total computation time! With the changes here
`FEProblemBase::initialSetup` no longer even appears in the graph, which
is how it should be.

I recall that I was forced to do derivative calculations by default for
the reasons stated in the comment I'm deleting. My memory says some
phase field object was initializing its material properties in its
constructor, or more likely during `initialSetup`, so we had to enable
derivative calculations then or else its results would be garbage.
Hopefully, however, if there are objects still doing things like that we
can do a little more fine-grained control to make their objects work
without significantly sabotaging everyone's performance.

Refs #14701

framework/src/base/MooseApp.C

@@ -352,6 +352,8 @@ MooseApp::MooseApp(InputParameters parameters)
   }
 #endif
 
+  ADReal::do_derivatives = false;
+
   Registry::addKnownLabel(_type);
   Moose::registerAll(_factory, _action_factory, _syntax);
 

framework/src/problems/FEProblemBase.C

@@ -349,11 +349,6 @@ FEProblemBase::FEProblemBase(const InputParameters & parameters)
     _num_grid_steps(0),
     _displaced_neighbor_ref_pts("invert_elem_phys use_undisplaced_ref unset", "unset")
 {
-  //  Initialize static do_derivatives member. We initialize this to true so that all the default AD
-  //  things that we setup early in the simulation actually get their derivative vectors initalized.
-  //  We will toggle this to false when doing residual evaluations
-  ADReal::do_derivatives = true;
-
   _time = 0.0;
   _time_old = 0.0;
   _t_step = 0;
@@ -5156,12 +5151,7 @@ FEProblemBase::computeResidualSys(NonlinearImplicitSystem & /*sys*/,
                                   NumericVector<Number> & residual)
 {
   TIME_SECTION(_compute_residual_sys_timer);
-
-  ADReal::do_derivatives = false;
-
   computeResidual(soln, residual);
-
-  ADReal::do_derivatives = true;
 }
 
 void
@@ -5449,6 +5439,8 @@ FEProblemBase::computeJacobianInternal(const NumericVector<Number> & soln,
 void
 FEProblemBase::computeJacobianTags(const std::set<TagID> & tags)
 {
+  ADReal::do_derivatives = true;
+
   if (!_has_jacobian || !_const_jacobian)
   {
     TIME_SECTION(_compute_jacobian_tags_timer);
@@ -5538,6 +5530,8 @@ FEProblemBase::computeJacobianTags(const std::set<TagID> & tags)
       _displaced_problem->setCurrentlyComputingJacobian(false);
     _safe_access_tagged_matrices = true;
   }
+
+  ADReal::do_derivatives = false;
 }
 
 void