Depends on the formation, and again, the realities of the theater.
Also, the problem with the US military during WWII is that, the theoretical rarely found any firm ground in the practical, and many handbooks for how to organize, command and equip the unit were thrown out or disregarded entirely by units and their commanders when faced by the reality of the situation. In short, a lot of American formations and tactics were improvised and in a constant state of flux and development; they went with what worked.
That being said, the trope of the Thompson being actually 'issued' to Rifle company NCOs is in fact, incorrect. A rifle company had six (6) M1A1 Submachineguns issued to it directly, whereupon they could then be given on a mission basis to the Rifle platoons, this decision would therefore nominally fall to the Captain or the Company First Sergeant. That being said, the plethora of M1A1s seen in the hands of Junior NCOs and Junior Officers can be explained in several ways:
They simply kept them, there are plenty of instances of units failing to report 'outside-of' or 'excessive' equipment on their TO&E as they were loathe to part with the extra firepower.
Casualties and resupply. Goes hand in hand with (1), I believe this is self-explanatory.
Formations, or presence of vehicles.
To elaborate on (3), you'll notice I mentioned a Rifle company in particular, other formations often had a much higher concentration of SMGs and Carbines than their rifle counterparts. An American rifle squad would, on paper, be equipped with 9-12 M1s (depending on squad size) plus a Squad Automatic Weapon (BAR). Later this would be increased to two BARs, etc.
US Airborne formations had easily twice the number of SMGs and Carbines due to their lighter formation and the assumption that they would be fighting for shorter amounts of time and in closer, more intense circumstances.
US Mechanized (e.g "Mounted") formations also had a plethora of M1A1s and M3 Submachineguns as they were considered OVWs "On Vehicle Weapons", and most M3 Halftracks, Trucks and Jeeps would have a Thompson underneath the driver's seat to this effect. There are several pieces of literature that lend evidence to this:
"Armored Infantry units used the same weapons as other infantrymen, but they were alloted somewhat differently. They were not issued .30cal Brownings owing to the Rifle Platoon's seven machineguns and five submachineguns [almost as much as a dismounted Rifle COMPANY]...Armored infantry units possessed more Thompson .45cal...SMGs....than any other unit these were issued to halftrack drivers..."
Three other publications provide excellent contrast between what a US mounted unit may possess in comparison to its Infantry counterparts, "Men on Iron Ponies" and "Through Mobility we Conquer" compare and contrast US reconnaissance units heavily with their infantry counterparts. Osprey's "WWII Cavalry Groups, Euro Theater" provides a reader with what a typical reconnaissance platoon would be equipped with:
As you can see, the rifle strength of the platoon is quite low, but its concentration of close-range, low penetration, rapid-firing weapons is high. This is an organization that attempt to anticipate what the unit in question is made to do (short and low-scale dismounted actions). Compare this to a Rifle Company, who's mission is to 'destroy the enemy.' Like the Germans in 1941, 42, the US Army did not fully anticipate the requirements for close-combat capable weaponry, and in this regard greatly over-estimated the rate of fire and effectiveness of both the BAR and M1 rifle in this regard.
Its probably what led to so many resourceful NCOs scrounging as much extra firepower as they could. In this case, doctrine eventually followed reason and near the war's end it was considered TO&E to give a Squad Leader some sort of lighter, high-rate-of-fire weapon. Nominally they therefore had little personal control over it, but often took the situation into their own hands. The Army, to its credit, realized it had gotten something wrong and decided to officiate the trend when it began to be noticed.
The "average officer" I'm assuming, is meant to mean Company and Platoon level.
In reality, things like unit equipment are pretty standardized across the Army through a system called Table of Equiment or "TOE". Big Brass and Senior NCO's usually created these TOE's and the Army would standardize them.
At the beginning of WWII the U.S. Army went through a massive reorganization to be more efficient and streamlined.. The Army consolidated all of it's logistics, supply, communications, under one umbrella command called the Army Services Forces. These commands would direct the "beans and bullets" aspect of fighting the war, to include training and doctrine.
These units would decide on what weapons to develop, procure, and distribute to the Army.
Using this equipment, senior leadership would create through trial and error TOE's, that could best distribute the equipment to the necessary units to project firepower and mobility based upon their unit type and purpose.
If you compare a standard infantry company TOE to that of a cavalry reconaissance troop, you'll see minor variations. If you go so far as to compare either of these to a Headquarters and Service company for an engineer combat battalion, you'll see a much larger variation in equipment.
Therefore, there is already a variation in what is nominally assigned and meant to be "on the books" for a unit; though combat action, theft, loss, logistical and personnel shortages, rarely made these 100% accurate at all times. Sometimes a unit would be over supplied with one item and be dangerously short of another.
These items could be bartered with other units who had complimentary shortages to fill in the gaps, and it's a universally well known trope that soldiers are master thieves when it comes to stealing another units equipment (I've personally pulled guard duty on pallets of MRE's and the motor pool at night when food and parts were in short supply in Iraq).
That being the background of what was expected of a unit and what an Officer, NCO, and Enlisted was expected to be equipped with. An Officer was issued as standard a sidearm, the Colt 1911 .45, or .38's for rear area units, M1 Garand's as the standard Army rifle. M1 Carbines were priority given to airborne units first with assignment as well as issued to mechanized infantry, engineers, and other support troops who were expected to be encumbered or have limited space. The Thompson was issued to NCO's and Officers as a priority as they were not expected to be main engagement troops and were to be giving support fire, or were issued for dense foilage areas such as jungle terrain. The M3 (the famous "grease gun") later replaced the Thompson because of it's weight and lack of penetration. The M3 would still be issued to tank crewmen as late as the 1980's. Finally the BAR or Browning Automatic Rifle was the standard infantry support weapon that the M249 serves today.
In all reality, an officer would not be interested in carrying an M1 Garand or a BAR. The BAR was meant to be a direct action weapon, while the officer would need to be pay attention to the entire fight. The M1 Garand could be heavy and bulky, and with the officer having to use radios, maps, compasses, etc., could be a burden, so they most often carried the Thompson or M1 Carbine. An officer would have little incentive to carry anything other than his sidearm and one of those two rifles.