diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index 8b9e56b39f75f..b44b83cec7b71 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -269,14 +269,12 @@ def _create_categorical(cls, data, dtype=None):
         return data
 
     @classmethod
-    def _simple_new(cls, values, name=None, dtype=None, **kwargs):
+    def _simple_new(cls, values, name=None, dtype=None):
         result = object.__new__(cls)
 
         values = cls._create_categorical(values, dtype=dtype)
         result._data = values
         result.name = name
-        for k, v in kwargs.items():
-            setattr(result, k, v)
 
         result._reset_identity()
         result._no_setting_name = False
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index de27f0c0be850..f1b6f5c6d43b4 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -164,12 +164,6 @@ def equals(self, other):
             # have different timezone
             return False
 
-        elif is_period_dtype(self):
-            if not is_period_dtype(other):
-                return False
-            if self.freq != other.freq:
-                return False
-
         return np.array_equal(self.asi8, other.asi8)
 
     def _ensure_localized(
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index ec95b6c483c52..64bbb2a53725f 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -387,18 +387,12 @@ def _formatter_func(self):
     # --------------------------------------------------------------------
     # Set Operation Methods
 
-    def _union(self, other, sort):
+    def _union(self, other: "DatetimeIndex", sort):
         if not len(other) or self.equals(other) or not len(self):
             return super()._union(other, sort=sort)
 
-        if len(other) == 0 or self.equals(other) or len(self) == 0:
-            return super().union(other, sort=sort)
-
-        if not isinstance(other, DatetimeIndex):
-            try:
-                other = DatetimeIndex(other)
-            except TypeError:
-                pass
+        # We are called by `union`, which is responsible for this validation
+        assert isinstance(other, DatetimeIndex)
 
         this, other = self._maybe_utc_convert(other)
 
@@ -407,9 +401,7 @@ def _union(self, other, sort):
         else:
             result = Index._union(this, other, sort=sort)
             if isinstance(result, DatetimeIndex):
-                # TODO: we shouldn't be setting attributes like this;
-                #  in all the tests this equality already holds
-                result._data._dtype = this.dtype
+                assert result._data.dtype == this.dtype
                 if result.freq is None and (
                     this.freq is not None or other.freq is not None
                 ):
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index 6fa7a7d3d4fb6..6cb4410d6a305 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -248,15 +248,13 @@ def astype(self, dtype, copy=True):
             return Index(result.astype("i8"), name=self.name)
         return DatetimeIndexOpsMixin.astype(self, dtype, copy=copy)
 
-    def _union(self, other, sort):
+    def _union(self, other: "TimedeltaIndex", sort):
         if len(other) == 0 or self.equals(other) or len(self) == 0:
             return super()._union(other, sort=sort)
 
-        if not isinstance(other, TimedeltaIndex):
-            try:
-                other = TimedeltaIndex(other)
-            except (TypeError, ValueError):
-                pass
+        # We are called by `union`, which is responsible for this validation
+        assert isinstance(other, TimedeltaIndex)
+
         this, other = self, other
 
         if this._can_fast_union(other):
@@ -309,7 +307,7 @@ def get_value(self, series, key):
             return self.get_value_maybe_box(series, key)
 
         try:
-            return com.maybe_box(self, Index.get_value(self, series, key), series, key)
+            value = Index.get_value(self, series, key)
         except KeyError:
             try:
                 loc = self._get_string_slice(key)
@@ -321,10 +319,10 @@ def get_value(self, series, key):
                 return self.get_value_maybe_box(series, key)
             except (TypeError, ValueError, KeyError):
                 raise KeyError(key)
+        else:
+            return com.maybe_box(self, value, series, key)
 
-    def get_value_maybe_box(self, series, key):
-        if not isinstance(key, Timedelta):
-            key = Timedelta(key)
+    def get_value_maybe_box(self, series, key: Timedelta):
         values = self._engine.get_value(com.values_from_object(series), key)
         return com.maybe_box(self, values, series, key)