Hold on, that's not what Appian says, or rather it's a misunderstanding of Appian's Greek:

καὶ αὐτὸν οἱ μὲν ἄρχοντες τοῦ στρατοῦ χωρὶς ἑνὸς ταμίου διέδρασαν ἐς Ῥώμην

And the leaders of the army fled from him to Rome, besides one quaestor

Ἄρχων is a funny word and its sense is not made clear in English. Whereas Latin would be quite clear in its terminology, using dux to describe the senior magistrate holding an army's imperium and then specifying the ranks of other magistrates and officers within the army, Greek has difficulty translating Roman magisterial and military offices, since Greek doesn't have many words for magistracies or generals. Ἄρχων is derived from the verb ἄρχω, which literally means "to be first," although its more usual uses are "to begin," and "to rule"--the reasoning here I think is obvious. The Attic word for the chief magistrates at the city is Ἄρχων, Archon--hence the eponymous archon, the archon basileus, etc. Other Greek dialects had additional words for their magistrates, but Attic usually just substitutes Archon for them. For example, the Ephors at Sparta are usually called the Ἄρχοντες--Latin does a similar thing with Gallic and Germanic leaders, calling what we would describe as "chieftains" principes, because Roman law simply doesn't have an analog. The point of this is that the Koine in which Appian is writing uses ἄρχοντες rather freely. It can mean any military commander, but more often the word is associated with political leadership--Ἄρχων is the standard Koine word for the Latin magistratus. It simply means an elected magistrate, particularly the senatorial magistracies. The inclusion of ἑνὸς ταμίου reinforces that--ταμίας, literally "dispenser, controller" (of payments, etc.) is the Greek word for the office of the quaestor, further specifying that Appian means magistrates. It is not surprising that Sulla had many senatorial magistrates with him--consular armies were generally accompanied by additional magistrates who served as various commanders, etc (just look at any page in Livy that discusses the marshaling of armies against Hannibal).

There were, however, plenty of other officers, and senatorial magistrates weren't usually involved in the careful deployment of military formations. Military tribunes, legates (although the military legate is mainly a post-Sullan office), and centurions all held important--if not the most important--positions of command. Plutarch mentions specifically two officers, Lucius Basillus and Gaius Mummius, as commanding the party sent to seize the Esquiline gate. On this occasion the Sullans, led by Basillus' party, broke into the city but were pinned down when the unarmed inhabitants of the area pelted them with stones and roof tiles (not as silly as it sounds--if you've ever seen ancient Mediterranean roof tiles, you'll know that they're more like chunks of flagstone stuck to your roof)--Plutarch says that Sulla personally marched to the front, grabbed a torch, and led his troops forward, with orders that his archers were to light their arrows on fire and launch them at the rooftops. Plutarch does not specify what office Basillus and Mummius occupied, but Appian does. Appian does not mention them during the first march on Rome, but he does mention Basillus (whose name should probably be Basilus, the cognomen of a branch of the gens Minucia. A later, younger Lucius Minucius Basilus is known to have been a legate of Caesar's and was praetor in 45, and Greek has this nasty tendency to duplicate the letter L in Roman names for some reason) during the Mithridatic War. During the battle of Orchomenus, Appian says, the army was afraid to attack the enemy's camp until a military tribune (ὁ τοῦ τέλους ταξίαρχος) named Basillus jumped over the wall and killed a man, at which point the army followed. This must be the same Basillus--Sulla's army that marched on Rome was the same army that crushed Archelaus at Orchomenus. Presumably Mummius was also a military tribune, which makes sense because during Sulla's day military tribunes commanded legions. In any case, even centurions found themselves in extraordinary commands sometimes, and could lead special contingents with some frequency. Caesar's fourth line at Pharsalus was composed of one cohort from each legion, and while we don't know who the overall commander was we know that a centurion named Crastinus, the former primus pilus of the 10th Legion, commanded a volunteer force of 120 men from his cohort on the far right. So there probably wasn't much of a command issue at all