What needs to be done:

• The _path of the Arrow itself is stored in normalized coordinates and not modified.
• Positioning is performed by the _patch_transform. This has to be recreated when chaning the position.
• It's probably best to store x, y, dx, dy, width in private variables so that they can be reused for recreating the transform.

This can be used as an example to start with:

import matplotlib.pyplot as plt
from matplotlib.patches import Arrow

fig, ax = plt.subplots()
ax.plot([0, 4], [10, 0])

a = Arrow(2, 0, 0, 10)
ax.add_patch(a)

# code for modifing the arrow goes here.

plt.show()

Given that the transform needs to be recreated, I would not expect updating to be any faster than removing and recreating the arrow.
Possibly, making the FancyArrowPatch more user-friendly could be of higher priority.

It seems indeed, that the use of Arrow should be discouraged or even deprecated, because it suffers from the transform distorting it. This is essentially never desired.

This issue has been marked "inactive" because it has been 365 days since the last comment. If this issue is still present in recent Matplotlib releases, or the feature request is still wanted, please leave a comment and this label will be removed. If there are no updates in another 30 days, this issue will be automatically closed, but you are free to re-open or create a new issue if needed. We value issue reports, and this procedure is meant to help us resurface and prioritize issues that have not been addressed yet, not make them disappear. Thanks for your help!

Probably still relevant