Yes it seem unreasonable to me. You actually make my case. If he has taken the time to "Cover his DNA tracks," and has covering his tracks on his mind, why then would he even think of taking the phone?
You say he "remembers he still has her phone on him." How did he end up with her phone on him in the first place? If we use your scenario of her being in jogging clothes, her phone would be attatched to her wrist right? After he removed her clothing and her phone, those items are on the ground, unless he males a conscious effort to put her phone in his pocket, and why would he want to do that?
I do believe he was pumped up and in a rush to get away, but not knowing,yet, I think it's fair to keep in mind if he is the "serial killer" type, it could have been just the opposite after he killed her, and could have been very calm and relieved.
Another thing to remember. MSM said that her phone pinged "off the tower next to the Mountain Barn." not 100 ft across the road , or in the parking lot etc.
If she was using FindMyPhone, (which we don't know, she could have been using ICloud which I have read in both cases can at times be up to two miles off, depending on Data/wi- fi connection) and it was totally accurate, that would have meant that her phone was right under the tower.
Hard to tell if the cam can see the road. I looked on Google Maps, and it looks close enough where it may have, but not sure.