Not the structure of these things. Presuming as media has been reporting Trump has basically just tossed the Biden changes (which were largely a reinstatement of Obama-era rules and reverting the 2018 Trump changes, barring some of the ones that lawsuits were lost over) and rolled back to the 2018 version, the way it works is more like this:

1. You have a specific person whose job is to function as a judge-analog for these hearings, and a specific person who functions as a prosecutor-analog. It's typically the Title IX coordinator and someone working under them. Under Trump rules, these are required to be different people while under Biden and Obama era rules your judge-analog and prosecutor-analog could be the same person.
2. The accused is allowed to have a lawyer present under Trump rules, and must have a faculty assistant familiar with the process if they do not have a lawyer. Under Biden and Obama era rules it was acceptable for a school to bar the accused from having a lawyer present or any other representation.
3. Yes, live hearings are required, but it's not what you're implying. Either party can request the hearing be done by teleconference if they don't want to be in the room for any reason. Normally it's only the accused, accuser, a lawyer or faculty assistant for the accused, prosecutor and judge analogs and possibly parents or corroborating witnesses if either party requests them present. There's no huge media spectacle like you're implying, it's normally a closed hearing.
4. Yes, cross-examination is required, but it's also not what you are implying. The accused is not allowed to ask questions directly and any questions have to be approved by the judge-analog before they can be asked. The main difference between Biden/Obama and Trump guidelines here is that the questions are asked and answered on the spot, rather than questions regarding testimony by the accuser being submitted in writing and allowing them as long as they need to write the most effective possible answers they can think of. Testimony of the accused has always been live and subject to questioning with no real guardrails.
5. Let's not forget that the standard for punishment in this case is at the strictest "clear and convincing" (more convincing than preponderance but less than beyond a reasonable doubt) and is often "preponderance of the evidence" (literally slightly more likely than not). The Obama/Biden guidelines were that the standard must be "preponderance".
6. The accused is required to have timely access to what they are being accused of and what evidence will be brought, so that it is possible to formulate a defense.
7. The accused is required to have access to the training materials used to teach faculty about these procedures and standards, so that the accused can know what to expect at all.
8. Under Trump guidelines, you cannot punish the accused until after the a finding is arrived at. You can make changes as needed for the comfort of the accuser before any hearing, but nothing punitive (for example you can change the schedules of one or both so they don't share classes, change housing arrangements, etc but not for example suspend someone for having been accused without a hearing and finding happening).

Most of these are pretty basic fairness and due process things.

I don't think you realize what Title IX guidelines were like under Obama, some of the shit that was allowed or expected. Like the accused having no guidance or representation through the process and in some cases explicitly not being allowed to have a lawyer. Not being allowed to know what evidence was being brought against them or even necessarily exactly what they were accused of until the hearing or very shortly before. Having faculty trained using training materials (which the accused was not allowed to see) that explicitly say that women never ever lie but that men will say whatever they need to, in a system where the margin to be found liable is slightly more likely than not (note I said men and women here and not accused or accuser, because the materials in question were explicitly gendered once the guy accused in one case sued to be allowed to see them). There was a case where a guy accused a girl, and after being informed of the accusation responded by accusing him so his accusation was deemed retaliatory and shut down while hers was allowed to proceed.