The Woman Who Fell To Earth didn't sell me on Jodie either. A new Doctor's first episode in New Who seems to take a standard approach. Doctor crashes to Earth, is still a bit concussed and confused from regeneration. Stumbles about a bit, accidentally encounters a villain, gains their wits enough to see the villain off, tries on their costume for the first time. Invite somebody they met along the way to be a companion.
When Tennant, Smith and Capaldi all did this it felt right somehow. You're still getting used to the new Doctor, but there's the odd moment here or there when they begin feeling like The Doctor. In the final confrontation between The Doctor and Tzim-Sha, I didn't feel it. Jodie just didn't have the gravitas to give a big speech, and scare off an alien threat. She came across as whiny rather then commanding.
The writing doesn't help either. This last series Doctor Who feels more like it's about a person and her mates in a TARDIS, rather than about a Time Lord and her companions. The writers seem to be trying to make it an ensemble piece. Nothing wrong with that to an extent, but The Doctor has to stick out and be different/more intelligent/more alien than his companions. Jodie feels like one of the gang too much. If anything, Bradley Walsh's character feels more like the leader of the group. Another example showed in The Battle of Ranskoor Av Kolos, when The Doctor ordered Graham to return to the TARDIS, and Graham refused. It made The Doctor look weak. Can you imagine that scene playing out with Eccleston, Tennant or Smith? No way they would've just let their companion refuse to return to the TARDIS on finding out they intended to kill. That was more about the writing than Jodie's performance of it, but it again underlined her lack of gravitas. Almost as if the writers were allowing for it.
Jodie does very well with the more light-hearted, childish alien aspect of The Doctor. But I don't think she has the ability to pull off the scenes were The Doctor needs to be assertive.