We should be able to - it is better english, however I put that and it wasn't accepted. We wouldn't say I thank to photography in English. You could also say "it is thanks to photography that I have all that I do" but I guess this would look different in romanian too

Edit: having re-read this sentence and your question, I believe mulțumesc is from the verb to thank and is literally translated 'i thank' whereas the more colloquial 'thanks' is mersi in Romanian

Think of it as "I thank [the activity of] photography for everything I have". What if one were to say "I thank football for everything I have"... It makes more sense - I used to have nothing, but I was a good footballer, and now I thank football for all I have.