diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
index 23c57105ca5e..37820593005e 100644
--- a/lib/matplotlib/axes/_axes.py
+++ b/lib/matplotlib/axes/_axes.py
@@ -2208,19 +2208,11 @@ def _convert_dx(dx, x0, xconv, convert):
                 x0 = cbook._safe_first_finite(x0)
             except (TypeError, IndexError, KeyError):
                 pass
-            except StopIteration:
-                # this means we found no finite element, fall back to first
-                # element unconditionally
-                x0 = cbook.safe_first_element(x0)
 
             try:
                 x = cbook._safe_first_finite(xconv)
             except (TypeError, IndexError, KeyError):
                 x = xconv
-            except StopIteration:
-                # this means we found no finite element, fall back to first
-                # element unconditionally
-                x = cbook.safe_first_element(xconv)
 
             delist = False
             if not np.iterable(dx):
diff --git a/lib/matplotlib/cbook.py b/lib/matplotlib/cbook.py
index 483039e337ba..8dc62259e8b5 100644
--- a/lib/matplotlib/cbook.py
+++ b/lib/matplotlib/cbook.py
@@ -1619,13 +1619,13 @@ def safe_first_element(obj):
 
 def _safe_first_finite(obj, *, skip_nonfinite=True):
     """
-    Return the first non-None (and optionally finite) element in *obj*.
+    Return the first finite element in *obj* if one is available and skip_nonfinite is
+    True. Otherwise return the first element.
 
     This is a method for internal use.
 
-    This is a type-independent way of obtaining the first non-None element,
-    supporting both index access and the iterator protocol.
-    The first non-None element will be obtained when skip_none is True.
+    This is a type-independent way of obtaining the first finite element, supporting
+    both index access and the iterator protocol.
     """
     def safe_isfinite(val):
         if val is None:
@@ -1657,7 +1657,7 @@ def safe_isfinite(val):
         raise RuntimeError("matplotlib does not "
                            "support generators as input")
     else:
-        return next(val for val in obj if safe_isfinite(val))
+        return next((val for val in obj if safe_isfinite(val)), safe_first_element(obj))
 
 
 def sanitize_sequence(data):
diff --git a/lib/matplotlib/tests/test_cbook.py b/lib/matplotlib/tests/test_cbook.py
index da9c187a323a..264db5dc9887 100644
--- a/lib/matplotlib/tests/test_cbook.py
+++ b/lib/matplotlib/tests/test_cbook.py
@@ -608,6 +608,18 @@ def test_flatiter():
     assert 1 == next(it)
 
 
+def test__safe_first_finite_all_nan():
+    arr = np.full(2, np.nan)
+    ret = cbook._safe_first_finite(arr)
+    assert np.isnan(ret)
+
+
+def test__safe_first_finite_all_inf():
+    arr = np.full(2, np.inf)
+    ret = cbook._safe_first_finite(arr)
+    assert np.isinf(ret)
+
+
 def test_reshape2d():
 
     class Dummy: