I'd say diplomats are important bureaucrats more so than politicians, but there is definitely a political nature to their job. The reason they are so important, is they provide the day to day contact point for the US to foreign governments. They are somewhat of a middle man in a sense, but its between two fairly large bureaucracies, and there is efficiency in having a dedicated person be the gatekeeper. Government officials tend to be busy and have schedules filled well in advance, part of an ambassador's job is to get themselves or other high ranking officials on the schedule. An Ambassador and their staff are often the negotiators or oversee negotiations in most cases, and the heads of state usually are only involved as ceremonial approvals. Ambassadors tend to have some level of status partly because they have clearance to high levels of government on both sides, and in more corrupt places they can peddle their influence for various bribes.
The less advertised part would be the ambassadors, and their diplomatic staff are the primary spies of every nation. Not every ambassador and every part of their staff is a spy, but significant portions are, and ambassadors at some level involved in the intelligence gathering activities.