Hmmm, well I guess we have very different experiences with management then. I work for a large care company in Amsterdam, I've never seen management 'roll up their sleeves' when there were shortages due to Corona. They just find new ways to pressure and cajole employees into working extra shifts (and thus putting themselves at risk more). They're not gonna show up to help shower elderly people, it's not in their job description.
You've never seen it because you dont work in demand planning or supply chain. You're taking literally "rolling up your sleeves" which again fits your physical work narrative as you definitely have a physical labour kind of job or work setting involving lots of people or hands on work. You got to think of putting in extra work as not always putting on overalls and work on a line with steel toe boots.
Management can only do so much too. Another bad assumption is a manager knows everything. Not true. He or she only knows so much and if they cant solve it they'll ask around someone else to help fix the issue. If SAP breaks down at the office, I'm pretty sure if I went to the VP of Finance saying SAP isn't working can you help me fix it, all he'd do it tell me to go to IT and have them look into it. That's why a boss values employees being proactive and trying to figure out stuff themselves instead of making a beeline to them when it's obvious they arent going to be the ones fixing it. But if lets say a few analysts quit, then the finance directors would have to get involved because they are shorthanded people and numbers analysis is something they can pitch in and cover. No finance managers are going to sit there and do nothing for two months as they re-fill the roles.
When account managers leave the company, it's not like sales or phone calls to customer head offices come to a grinding halt. Someone fills in and it'll be their manager until a new person is hired. Another account manager will likely not fill in unless they are asked to permanently take over the role because they dont want rotating account managers filling in for a month. And more importantly they dont want another acct manager knowing the details which they can use to their advantage for their own accounts.
When there's major shortages and the DP/SC guys cant secure product or materials, management can take the reins and try to secure it. Due to shortages, you cant make product out of nowhere and machines can only make stuff so fast. In these cases, someone will be cut product.
But what happens is upper management will negotiate to try to secure content from external suppliers. And if it's internally made content they can chat among themselves as regional factories and offices and redirect supply to other countries.
For example, most of out stuff is made in the US where I work. Due to covid shorts, its up to our team to take proactive measure to get as much stuff up here to Canada or else there's good chance the US wont give a shit about us. Then it becomes a "split the pie" game of who gets how much. And that's management's call. It's even tougher to split the pie because some of the stuff is specific to country. So if the US goes on a manufacturing binge and it's a product specific to US markets, we'd get nothing. Then they'd say something like "Well, you should had talked to us earlier".
Joshmyersbv above gave you a special chip shortage cut example of management stepping in, yet you purposely ignored it.