I think players in the high 80s (around 87 and up) can safely be set at "getting tired" without a detrimental or significant drop off in performance, as I understand the rating.
I think you may be misunderstanding the rating. At the very least, you would seem to have a very different understanding of it than I do. As I understand it, the drop in performance (such that it is) happens for all stamina levels equally, it just varies when it happens.
For example, that 87+ stamina guy is going to suffer from playing at "getting tired" or whatever level the same way a 70 stamina guy is. At the precise moment they switch over to the "getting tired" level, both will be performing at the same x% of efficiency.
What varies is *when* that player falls into the "getting tired" level. For the 87+ stamina guy, maybe he can go 12 minutes without being subbed and stay within the "fairly fresh" zone (although, to be clear, I think there are level of fatigue within each zone). The 70 stamina guy can maybe go 7 minutes before be hits the "getting tired" level.
I think of it this way (numbers and % are for illustration purposes only) -
Tip-off: 87+ Stamina guy (100%); 70 Stamina guy (100%) (both fairly fresh)
2:00 Minutes in: 87+ Stamina guy (96%); 70 Stamina guy (93%) (both fairly fresh)
5:00 Minutes in: 87+ Stamina guy (90%); 70 Stamina guy (85%) (both fairly fresh)
9:00 Minutes in: 87+ Stamina guy (80%); 70 Stamina guy (72%) (87 - fairly fresh, 70 - getting tired)
15:00 Minutes in: 87+ Stamina guy (62%); 70 Stamina guy (45%) (87 - getting tired, 70 - tired)
20:00 Minutes in: 87+ Stamina guy (40%); 70 Stamina guy (10%) (87 - tired, 70 - very tired)
So, at the precise moment they two players transition from any one zone to the next, they are operating at equivalent efficiency. For 87+ guy though, that would occur just after the 9:00 mark in the illustration above. For the 70 guy, that occurs earlier, perhaps around 6:30 minutes in or so.