diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index 06bf2e5d7b18e..5fae48ae5d4b2 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -99,9 +99,6 @@ class Block(PandasObject):
     __slots__ = ["_mgr_locs", "values", "ndim"]
     is_numeric = False
     is_float = False
-    is_datetime = False
-    is_datetimetz = False
-    is_timedelta = False
     is_bool = False
     is_object = False
     is_extension = False
@@ -213,11 +210,6 @@ def is_view(self) -> bool:
     def is_categorical(self) -> bool:
         return self._holder is Categorical
 
-    @property
-    def is_datelike(self) -> bool:
-        """ return True if I am a non-datelike """
-        return self.is_datetime or self.is_timedelta
-
     def external_values(self):
         """
         The array that Series.values returns (public attribute).
@@ -547,7 +539,8 @@ def _maybe_downcast(self, blocks: List[Block], downcast=None) -> List[Block]:
 
         # no need to downcast our float
         # unless indicated
-        if downcast is None and (self.is_float or self.is_datelike):
+        if downcast is None and self.dtype.kind in ["f", "m", "M"]:
+            # TODO: complex?  more generally, self._can_hold_na?
             return blocks
 
         return extend_blocks([b.downcast(downcast) for b in blocks])
@@ -634,13 +627,12 @@ def astype(self, dtype, copy: bool = False, errors: str = "raise"):
                 raise
 
         newb = self.make_block(new_values)
-        if newb.is_numeric and self.is_numeric:
-            if newb.shape != self.shape:
-                raise TypeError(
-                    f"cannot set astype for copy = [{copy}] for dtype "
-                    f"({self.dtype.name} [{self.shape}]) to different shape "
-                    f"({newb.dtype.name} [{newb.shape}])"
-                )
+        if newb.shape != self.shape:
+            raise TypeError(
+                f"cannot set astype for copy = [{copy}] for dtype "
+                f"({self.dtype.name} [{self.shape}]) to different shape "
+                f"({newb.dtype.name} [{newb.shape}])"
+            )
         return newb
 
     def _astype(self, dtype: DtypeObj, copy: bool) -> ArrayLike:
@@ -2089,7 +2081,6 @@ class DatetimeTZBlock(ExtensionBlock, DatetimeBlock):
     values: DatetimeArray
 
     __slots__ = ()
-    is_datetimetz = True
     is_extension = True
 
     _holder = DatetimeArray
@@ -2167,7 +2158,7 @@ def get_values(self, dtype: Optional[DtypeObj] = None) -> np.ndarray:
     def external_values(self):
         # NB: this is different from np.asarray(self.values), since that
         #  return an object-dtype ndarray of Timestamps.
-        # avoid FutureWarning in .astype in casting from dt64t to dt64
+        # Avoid FutureWarning in .astype in casting from dt64tz to dt64
         return self.values._data
 
     def fillna(
@@ -2208,7 +2199,6 @@ def _check_ndim(self, values, ndim):
 
 class TimeDeltaBlock(DatetimeLikeBlockMixin):
     __slots__ = ()
-    is_timedelta = True
     _can_hold_na = True
     is_numeric = False
     _holder = TimedeltaArray
diff --git a/pandas/core/internals/concat.py b/pandas/core/internals/concat.py
index 01d8cde3e9af2..c65d104021a47 100644
--- a/pandas/core/internals/concat.py
+++ b/pandas/core/internals/concat.py
@@ -12,7 +12,6 @@
 
 from pandas.core.dtypes.cast import ensure_dtype_can_hold_na, find_common_type
 from pandas.core.dtypes.common import (
-    is_categorical_dtype,
     is_datetime64tz_dtype,
     is_dtype_equal,
     is_extension_array_dtype,
@@ -295,8 +294,6 @@ def get_reindexed_values(self, empty_dtype: DtypeObj, upcasted_na) -> ArrayLike:
                     # TODO(EA2D): special case unneeded with 2D EAs
                     i8values = np.full(self.shape[1], fill_value.value)
                     return DatetimeArray(i8values, dtype=empty_dtype)
-                elif is_categorical_dtype(blk_dtype):
-                    pass
                 elif is_extension_array_dtype(blk_dtype):
                     pass
                 elif is_extension_array_dtype(empty_dtype):