Entry seems pretty fast to me. The pinyin system means that you can enter a few letters using the English alphabet and it will show you the most likely character. For common words, one or two letters per character is enough. I am not a native Chinese typist, but even by guessing at the proper spelling, the predictive entry system is good enough for me to type at a non-too-terrible speed.
Not a native speaker either, but I hate typing in Pinyin on a touchscreen device (iPhone in my case). You have to get almost every letter right, whereas if you type English and miss up to 50% of the letters, autocorrect can usually still save you. I agree that Pinyin feels pretty much as fast as typing English on a real computer, though.
(German is also incredibly frustrating to type on a phone, as there are more ways to compose words than autocorrect could ever possibly know.)
I find it very surprising you have said pinyin is slow. It has the downside that you need to look at what you're typing, but it's certainly not slow. With modern IMEs it's more akin to something like Swype in it's usage.
I am appalled when in other regions in China where they do not use pinyin, watching people spending over a minute trying to tell their friend that they just got on the train.
