The question of where to conduct a pre-takeoff engine run-up when no dedicated run-up area exists touches on a practical gap between pilot training and real-world airport operations. At many smaller towered and non-towered airports, run-up boxes are a standard feature near the threshold, but runway configurations, taxiway geometry, or construction can leave pilots without a designated spot. The standard procedure in the absence of a run-up area is to hold short of the runway hold short line, advise the tower that a run-up is needed, and complete the checklist before calling ready for departure. At towered airports, this is generally accomplished by simply not calling "ready" until the run-up is finished, though pilots should be proactive in advising ground or tower of their intent so controllers can sequence traffic accordingly.
The communication dimension is where many pilots, particularly those transitioning from light training aircraft to more complex or turbine equipment, encounter friction. Tower controllers at busy airports operate on compressed timelines and expect aircraft to be ready for departure when they reach the hold short line. Calling ready before completing run-up checks, or blocking a taxiway while performing them without advising ATC, creates sequencing problems and can generate the kind of controller frustration the original poster describes. The professional standard is to communicate early: advise ground control during taxi that a run-up will be required, which allows the controller to build that delay into their sequence rather than being surprised at the hold short line. This is standard practice for crews transitioning through unfamiliar airports.
The traffic-behind-you concern is operationally significant and situationally dependent. At airports with a single taxiway leading to a runway threshold, an aircraft stopped for run-up can effectively block all subsequent departures. In this scenario, pilots should coordinate with tower to either pull to the side if pavement width permits, or accept that a brief hold is necessary and communicate its expected duration. For turbine crews, pre-takeoff checks are typically abbreviated compared to piston run-ups, often taking under a minute, which reduces the impact. Piston pilots performing full mag checks, carb heat, and systems verification may need two to four minutes, which changes the calculus when a line of aircraft is forming behind them.
The IFR versus VFR distinction the original poster raises is real but nuanced. IFR departures at towered airports typically involve a clearance that has already been received and read back, and the pilot is expected to be ready to depart expeditiously once cleared onto the runway. Controllers issuing an IFR clearance are often coordinating a departure window with approach or center, and a delay at the hold short line can cause that window to close, resulting in a revised or void time clearance. VFR departures carry less rigid time constraints in most cases, but at busy Class C and Class D airports, any delay at the threshold affects the efficiency of the traffic flow. In both cases, the professional mitigation is the same: communicate the need for a run-up early, complete it off the active surface if any taxiway width permits, and call ready only when truly ready to roll.
For operators flying Part 135 or corporate Part 91 missions into smaller regional airports, this scenario is common enough that it warrants inclusion in crew resource management and airport familiarization briefings. Airport diagrams in Foreflight, Garmin Pilot, and similar EFB platforms will show run-up areas where they exist, and their absence on the diagram is itself useful pre-departure information. Crews who identify the lack of a run-up area during taxi planning can sequence their checklist flow to complete as much of the pre-takeoff check as possible while still moving, arriving at the hold short line with only the final engine checks remaining. This is the kind of operational discipline that separates efficient professional crews from those who create unnecessary delays and controller workload at unfamiliar airports.