That feeling that you can't run at full speed is common in that kind of role but working in startups or other small co's you can have just as much or more dysfunction: you can run yourself ragged or feel like you're in a magically productive team or even both at the same time.
I have two relatives who work at a major online retailer that has 'Z' in the name and one of them is thrilled to go to work each day and the other just had a nervous breakdown because they had her doing three people's roles. The situation you have where you feel unproductive but the people around you think you are is pretty common because of the economics of scale: if you are working at a 100x bigger company that software you work on can have 100x the economic impact that it would for the smaller company. So a big company can have an organization that seems unproductive based on your instincts working at small companies but you are creating enough value to pay you so you are doing fine. [1]
If you have some slack, don't feel bad using it in a way that is meaningful and restorative to you and keeps you in fine condition to do what your organization needs of you.
[1] A friend of mine quoted Marx and said I was being ripped off because I was getting paid less than the value I made and I told him... I've tried the alternative and it usually ends up as hell on Earth.