If the company is small enough, and the all-hands frequent enough, those awards become a 'who haven't we given an award to yet', which ultimately undermines the point of giving it out in the first place.
My point was just that it can be tedious/demoralizing for people who aren't eligible to be called up.
It's very tempting to phone it in while looking for another job. It's basically a meeting for QA and manufacturing to remind everyone about QA and manufacturing.
My employer's (large commercial software company) award system is peer-based - anybody can suggest an award, from simple kudos up to multi-thousand dollar awards. Kudos don't require approval and are typically announced in weekly or monthly team meetings. The larger things are announced in the division or company-wide meetings, as appropriate.
The system actually doesn't allow generic team awards. It can be a bit annoying, but it also prevents what you describe. If I want to recognize a team, I have to call out each person individually.
As a project manager (but with no direct reports), I try to award a few kudos per quarter, just to let my peers (including all the teams I work with regularly, that's 50 developers/testers) know I'm paying attention. I typically submit a few larger awards per year. So far, I haven't had any outright rejected by my director or VP, only the level adjusted (both up and down).
Edit - another thought - I also proactively seek feedback from product management and sales. It doesn't take a lot of feedback to make a difference in team morale. While my teams are directly client facing, it's not difficult to obtain client feedback that is directly relevant to my projects.
Why would it matter, surely you award those who've acted exemplary regardless of prior awards. A company that handed out rewards in any other fashion would be unusual, wouldn't it?