My biggest question is, for them to charge him with murder, doesn't there have to be undeniable physical evidence proving that 1) Alexis lost an unrecoverable volume of blood, 2) There is enough physical evidence to place her in his trailer and his DNA physically returning her car to the lot.
No, not necessarily.
For a MWAB (murder without a body), you DO need to prove that the person is dead beyond a reasonable doubt, but there are ways to do that besides having a large amount of blood or something like that.
Here are some of the ways that a prosecutor can prove the person is dead, without needing a large amount of blood or brain matter or whatever:
- Certain bodily fluids are only released when a person is dead. Those fluids being present mean that a (decomposing) corpse was in the house at some point.
- Cadaver dogs hit on the house.
- There is physical evidence that points to a violent - and presumably fatal - altercation. In this case, Alexis's eyelashes, torn hair extensions and fake nail (which were all found in Taylor's camper) prove there was a violent struggle. If a large amount of blood (but not necessarily enough to say conclusively that the person is dead) was found, that also backs up the theory that the victim lost their life in a violent manner.
- The person's disappearance is 100% out of character. It helps if the person was a devoted parent, had something big to look forward to (a wedding, graduation etc.) In this case, Alexis was very involved in social media, but her accounts had no more posts on them from after the moment she disappeared.
- The circumstances of their disappearance would lead a reasonable juror to believe that the person is dead. There was one case on CharleyProject where witnesses had seen the woman (whose name I can't remember) being beat up and then thrown into a car by her boyfriend, who then sped away with her. She was never heard from again. Her body wasn't found for years, but said boyfriend was soon convicted of her murder and eventually led police to her remains.
- The defendant has a history of violence against people fitting the victim's profile (say, against girlfriends, teenaged girls etc.). If you have a history of beating up your girlfriends and one of them ends up mysteriously disappearing, chances are that it was probably because of you.
- You can prove that the person is capable of extreme violence, had the opportunity (no alibi), and you can establish a believable motive.
- You can establish a pattern. Unless you're really unlucky, two teenaged girls you know don't disappear under suspicious circumstances immediately after being seen talking to you. Most people don't know one person missing under suspicious circumstances, let alone two.
There are a few other things prosecutors can use to prove a missing person is dead, but I don't want to bore anyone, haha. Hope this helps.
ETA: In Alexis's case, you have points #3, #4, #5, #7 (the alibi and probably motive parts), and #8. I don't know if cadaver dogs were ever used.