Support the idea heartily. This mechanic allows even downgrading some zombies and make hordes a challenge by sheer numbers instead of being outright dangerous as individuals, you just would have to manage your strain levels and that limits how much of the horde you can hack away one-by-one in given time.
This would also give more use to temporary boosts such as energy drinks or amphetamines - they would push away (some of) the strain for some time, but after a while you’d start getting strained much easier.
This could also partially overlap the “Tiredness” system. If youre tired you also strain faster. Also the sickness system could manifest itself trough straining/being easily strained.
So this could be like: one stat for outright physical stress (cure : rest, take a break, eat, stop doing physical stuff for a while) and other stat for “maluse of body/cumulative strain” ((partial)cures: Sleep well, rest really good, medicines, being well fed, let yourself recuperate over prolonged time).
Once the outright physical stress is up and you dont rest/take it easy you start adding to the maluse-figure. If you take stimulants you remove immediate physical stress but move it to “maluse” figure instead. The higher the maluse figure is the more easily and more dramatic effects will occur upto the death of character simply from sheer exhaustion.