diff --git a/arraycontext/impl/pytato/__init__.py b/arraycontext/impl/pytato/__init__.py
index f7f7be8d..337a70ea 100644
--- a/arraycontext/impl/pytato/__init__.py
+++ b/arraycontext/impl/pytato/__init__.py
@@ -116,6 +116,10 @@ def _preprocess_array_tags(tags: ToTagSetConvertible) -> frozenset[Tag]:
 # }}}
 
 
+class _NotOnlyDataWrappers(Exception):  # noqa: N818
+    pass
+
+
 # {{{ _BasePytatoArrayContext
 
 class _BasePytatoArrayContext(ArrayContext, abc.ABC):
@@ -338,14 +342,6 @@ def _rec_map_container(
         def _wrapper(ary):
             if isinstance(ary, allowed_types):
                 return func(ary)
-            elif not strict and isinstance(ary, self._frozen_array_types):
-                from warnings import warn
-                warn(f"Invoking {type(self).__name__}.{func.__name__[1:]} with"
-                    f" {type(ary).__name__} will be unsupported in 2023. Use"
-                    " 'to_tagged_cl_array' to convert instances to"
-                    " TaggableCLArray.", DeprecationWarning, stacklevel=2)
-
-                return func(tga.to_tagged_cl_array(ary))
             elif np.isscalar(ary):
                 if default_scalar is None:
                     return ary
@@ -353,7 +349,7 @@ def _wrapper(ary):
                     return np.array(ary).dtype.type(default_scalar)
             else:
                 raise TypeError(
-                    f"{type(self).__name__}.{func.__name__[1:]} invoked with "
+                    f"{func.__qualname__} invoked with "
                     f"an unsupported array type: got '{type(ary).__name__}', "
                     f"but expected one of {allowed_types}")
 
@@ -585,6 +581,24 @@ def _thaw(ary):
             self._rec_map_container(_thaw, array, (tga.TaggableCLArray,)),
             actx=self)
 
+    def freeze_thaw(self, array):
+        import pytato as pt
+
+        import arraycontext.impl.pyopencl.taggable_cl_array as tga
+
+        def _ft(ary):
+            if isinstance(ary, (pt.DataWrapper, tga.TaggableCLArray)):
+                return ary
+            else:
+                raise _NotOnlyDataWrappers()
+
+        try:
+            return with_array_context(
+                self._rec_map_container(_ft, array),
+                actx=self)
+        except _NotOnlyDataWrappers:
+            return super().freeze_thaw(array)
+
     def tag(self, tags: ToTagSetConvertible, array):
         def _tag(ary):
             return ary.tagged(_preprocess_array_tags(tags))