A shapeshifter can use this to a great advantage. Imagine a virus or bacteria infecting you. It's bad, because you're the optimal conditions for this virus or bacteria to spread.
And then you change the game.
Change into a creature that is unaffected by that particular virus or very good at beating the bacteria. Cold-blooded, warm-blooded, living together with it (bats!), having crude but effective immune systems, or simply being slightly different can turn the tide in a short time. Very few sicknesses or parasites can get a hold on you.
Healing damage is also easy, as you morph anyway. With such drastic changes, healing a wound at the same time seems trivial.
The psychology seems to be the greatest problem. How do you change into something else without losing brain power? Humans are the pinnacle of intelligence, understanding, planning and memory. Changing to a tiger will make you stronger, but jow can you still remember to tie your shoes? Taking the brain power with you is a difficult task, as the human brain is specifically grown in a very large head. Cramming that in other species that are certainly not optimised for it can lead to major problems.
If this is solved, you still need to grow a lot of muscle menory. Sure you can probably grow it that normal walking, running, flying or whatever is required works, but you'll not be optimised. Imagine changing into a human and be presented cutlery. Could you really use it? I mean the first so many times I was eating with sticks was incredibly challenging. That and a thousand tiny things are learned in years growing up. Changing into different creatures will mean you miss all that. All creatures you control will be basic in that control sense.
Finally you might lose identity. Who you are and what you are keep us grounded. If you change regularly, you need to have a special kind of mindset to not go completely bonkers.
How far does the change go? Where do chemicals and nutrients go? If you eat grass as a cow, what will happen to the food in the 4 stomachs when changing? Where does the venom of a snake go? What happens to the dead stuff like hair and nails when changing? Where does extra mass go, or if you don't have enough? How do you power all this? Much can easily be handled by suspension of disbelief, as these kinds of strange things happen in fiction all the time. Yet it us worth mentioning.