The RTE has the perfect position within a scaled project for combining Project Management activities with Agile Coaching, Consulting and Leadership. Potentially a Solution Train Engineer (STE) could compete in that matter with a RTE, but - besides some differences in responsibilities and that the STE is much rarer on the job-market - RTE is the role established right at the border to the more classical, but still within the Agile part of the setup. Hence, for people (like me), who love Project Management as an academic discipline and love doing the hands-on Project Management work, too, the role RTE has quite a very satisfying character.
On top, you, as RTE, have got the honour to constantly promote - sometimes even fight! :D - for the agile way-of-working, which is usually described in job descriptions as foster agility or protecting the agile way-of-working. 

As RTE you are a servant leader to different circles of people. Hence, you will wear different hats:
The RTE is by definition a servant leader of the ART: As part of the Product-Management Team (Product Manager, System Arcitect and RTE) you do lead the people of your train in many different situations: organizationally, administratively, processorial, methodological, and maybe the most important: mentally, in advancing line and mode of thinking, transformationally and progressively. (Wow, really, that's responsibility!). You do that with team members, architects, developers, Product Owners, Businesss Owners, and other roles and people. Since an ART usually consists of 40 to 150 people, your direct and indirect impact is or could be (it should be! :) truely formative.
As RTE you are in a very good position to lead a team of coaches, for example Scrum Masters, Agile Coaches, Team Coaches. Here you can shine with your team-leading qualities in a closer relationship with a smaller group of people, of who you might even be a disciplinary manager, too.

Additionally, as RTE you regularly jump-in for your Product Manager(s) *), PM, in case of their absence in several briefings, meetings and ceremonies. The PM usually leads the train with respect to the technical path and the product vision. As the voice of the customer the PM is the one who keeps an eye on the market development, adjusts direction of the product (-features) and hence has an important strategic role. Of course, as full-time RTE you wont be able to cover all these responsibilities of the PM completely, but you both are in a very close exchange with each other and that usually makes you the person, who's best up-to-date in the topics on the PM's desk: together you manage the backlog in prioritization-meetings, you share stakeholder management activities, you discuss and define the topics of organizational and transformational development for your perimeter.
You, the RTE of the PM-Team, are seen as one team by the train-members. That "esteem" or reputation is projected onto you as RTE as well, when you recurrently back-up your PM.