I agree with
@JackLumber, and would go further yet: for "could easily", substitute "would probably". The HRE was very decentralised both because of its geographic extent and because of the tug-of-war between Emperor and Pope over primacy (and specific authority and privilege in a million little cases). If you have "only" a German Kingdom, then that is far more coherent politically. Its Southern border is well-defined (look at those nice mountains!) and it has not ultramontane entanglements of either the temporal or the ecclestiastical kind. Meanwhile, it is Catholic in the same way the France is, but the lack of an imperial claim averts the whole Investiture Controversy. (The Pope will be spending the same energy, in this ATL, instead doing his best to boss the rulers of Italy around.)
I would expect Germany to do rather well, especially since France has issues of its own. (Specific issues may be butterflied, but I don't expect this to be a scenario where France rolls sixes every time.) I would expect Germany, free here to prioritise its own interests without having to give a single damn about Italy, to push its Western border up to the Somme. Further to the South, Germany and France may at some time even work together against Burgundy, with France getting the bigger share (and Germany annexing roughly the area of OTL's Switzerland). This would then settle the border between Germany and France, probably rather permanently.
Germany's main drive, as in OTL, would be to the East. With no non-German concerns or interests, the German drive into Pomerania, Prussia, Bohemia, Austria, the Pannonian Basin and the Transylvanian Plateau would presumably be somewhat bolstered and accelerated.
While, I do not deny that perhaps the German kingdom would be better in some regards, do you also deny the immense positives in ruling the kingdom of Italy in imitation of their founders, Pepin, Charles I and so forth? For a Frankish king of that period, there is little reason to be a petty king and not extend yourself universally. The German kingdom is a fundamentally Frankish lordship, not a Normano-Anglo state, that is subdued in its claims relatively. Italy also in addition to affording legitimacy value to the Frankish monarchs of the empire, also provided large amounts of dues for the empire. Even times of Papal supreme authority in the Medieval Era, feudal states across Italy were paying dues to the Emperor, even within the Papal allodium. As I mentioned elsewhere, the Papal-Imperial dispute was simply as Urban II mentioned or referred to in 1090, that 'some tend to matters not of their own and seek to infringe upon matters related to the Church.' Likewise, the Emperors sought to dispute the fundamental authorities of the Papacy in matters pertaining to legal defining, rendering and appointment. This was a conflict that the Papacy could not avoid.
As such, what I am approaching, is that even if the East Francian kings never touched Italy, if they continued to reject Papal mandates and legal defining, they will come into blows with them regardless, but with a smaller force to fight with from Germany than the immense armies that Otto IV and Frederick II were able to derive from a polyglot and diverse empire (which the Papacy met in battle with armies of an equally diverse Italo-Frankish-Occitan-Norman background). As we know, the Papacy is not adverse to battling many lord of Europe at the same time and surely does not seem int eh slightest afraid of their armies arrayed. Often, the Papacy was engaged with the Empire, England, Venice, the County of Toulouse, Kingdom of Aragon, Kingdom of Norway and then on top of this, dealing with matters pertaining to crusades and so forth. Germany will be even more powerless to oppose the Papacy int eh open field of battle than otl and will constantly be under threats if they choose to breach traditions on matters. Perhaps though, in this position, Germany will become more submissive to the Papacy.
Regarding the wars with France, much of French victories against the Empire, I interpret as victories obtained partly via Papal assistance. When Philip II defeated the army of Otto IV, he was waving the flag of the Crusades, deposing a heretical apostate who had overstepped the traditions and exceeded the limits; becoming both a tyrant and a man who breaks his own word. Otto IV was already bloodied after facing utter defeat in Spoleto against the Papal crusader army under Innocent III and then his defeat certainly inspired the defection of much of the German princes to the Papal faction holding Frederick II, the so-called Staufen faction long arrayed against the Papacy, now became the Papal allies and agents in Germany and Innocent III nullified the German election and nominated ex cathedra Frederick II, with the support of the vast majority of the eastern, so-called Saxon princes. As such, Otto IV went to battle with Philip II with an army drawn from his dwindling support; hence his necessity to seek support from king John Lackland of England, who though embattled, was at least not so thoroughly shamed in Italy as Otto IV was. France was on the other hand, seen by Innocent III as the perfect monarchy, they were seemingly loyal to the Papacy, Frankish and did not infringe upon Papal feudal power over Europe, instead, French monarchs of the Capet instituted a direct cooperation with the Papacy. Even the peasantry in the main areas of France, seem devoted to the Papacy and his dictates to a degree in excess of most areas of Europe. All of this led later pontiffs to describe the French monarchy as the sublime state, the most preferred realm in Christendom, etc...
However, note, France was not seen as ideal simply due to their lack of Italian holdings. It was their devotion and acquiescence to Papal authority that assured them. If the French ruled all of Italy as Kings of Italy, and they took the same policy that they did in France, not impose any dues upon the Papal holdings directly and submitted to Papal commands, the Capet kings of Italy would receive the same paternalism from the Papacy as otl, which oddly led to Papal mistakes (such as the inquisition, one of the most major recessions of Papal power in Europe).
