Same experience. The "government = inefficient" propaganda has been repeated ad infinitum for decades so that now it feels like a law of nature to people. My experience is however that every large org is inefficient in its own unique way, no matter which sector.
Profit in it of itself is an inefficiency. It's a bandaid for the fundamental problems of the private sector. The fact the public sector isn't burdened by a requirement to make profit isn't a downside, it's a super power.