The more air you I push, the easier the exercises are for me. At the size of a full straw, I may as well be open mouthed, but with limited air, I find myself needing to find a softer volume level and I really need to hook my voice to my breath, just to generate sounds at all. That said, I do have a notch that forces me to lose air pretty fast - 7x faster than without a notch - so the smaller straw may just be to strengthen around the notch and not be so breathy sounding.
Glad it's working for you, sounds like you have a creative therapist!