Arb clock is based on service time, so it only counts days in the majors.
Let's game this out and say the Tigers promoted Jackson Jobe in 2021, but sent him down after one start. He only gets one day of service time, but if he was injured in Spring Training in 2022 before he is sent down, he would need to go on the Major League IL because he spent time on the active roster. I don't think he was, so he spends the whole year burning Option 2. Ditto 2023 and 2024 (he would be eligible for a fourth option). So in summary, he would be out of options now but wouldn't have much more service time. The spring training option/injury restriction is a service risk, especially for a pitcher, but only applies if they spent any time the previous year in the Bigs. (That is why Ty Madden is on the 60 day IL but Mattison was optioned).
There is also the salary component. 40 man players who have been in the majors are guaranteed at least $125K (that number goes up every year and I don't remember the exact number). That is much higher than the minimums at each level on the way up.
And when I talk about tying up a 40 man spot, remember this when the Tigers are pulling their hair out over who to DFA toward the end of the off-season. Mason Englert would come in handy right now, wouldn't he? If Jobe was pre-emptively added, maybe they don't have room to claim Tyler Holton, or they drop somebody else on the back end before they can come up.