I don't think that the view is necessarily correct. The natural consequence of any war is financial and military strain, however Justinian's conquests also brought a great deal of wealth to the Empire. The Byzantine military was almost constantly strained as they had to oppose a large number of enemies on opposing ends of the extremes of their empire. Thus the constant bribery and diplomacy for which the Byzantines became famous. The conquests had a number of positive affects with the great influx of wealth and growth of trade. More important might have been the export of Byzantine culture to far flung regions of the world a revival of the Rome of old. You are correct in a certain manner that his grandiose vision of reestablishing the Roman Empire and remaking Constantinople into the grandest city of the world weakened the empire, but in an indirect and unintended manner. His massive spending didn't become a problem until the plague struck in 541 A.D. which crippled both the Byzantines and their chief rivals the Sassanids'. At its peak the plague is estimated to have been killing as many as 5,000 people a day in Constantinople alone and have wiped out 40% of the city's population by its end. This plague left the empire a shell of its former self and incapable of resisting the resurgence of the Goths and later Lombards in Italy. The Byzantine Empire would enter a state of decline and territorial reduction not stopped until the 9th century. Really its a matter of exceptionally bad timing, no one had anticipated such an event and the loss of tax revenue from the dead was a huge blow. Unable to field an adequate army and unable to generate the money necessary to offset this lack of an effective field force the Byzantines were cut off at the knees. So I personally don't think it's fair to give so much blame to Justinian for the almost stunning decline of the empire's fortunes he did, after all, come remarkably close to seeing his vision become a reality. That they put a strain on the empire is undoubted, but without the plague such a strain would never have become unbearable and the empire might very well have comfortably recovered and continued its hegemony. The plague is to blame for the precipitous fall and turn of fortune of the Byzantines in the mid 6th century not Justinian's rather grandiose vision.

It is very fashionable to bash Justinian right now and I think historians are entirely right to do so, if they do it in a very qualified way. Justinian's wars up to 540 were clearly major successes, however after that his western wars only made a bad situation (due to the plague and the war with Persia) worse - Byzantine interests in relatively stable and highly Romanised regions such as North Africa and Italy were heavily damaged by long-term dissent and ongoing warfare, which definitely harmed the long-term benefit of these wealthy regions to the empire. Though the earlier part of the reconquest was relatively smooth, Justinian's mismanagement of these new territories for the next two decades were instead detrimental. I'm not saying that it was his entirely his fault, but it is clear the wars and their aftermath could have been managed better. North Africa was a fabulously wealthy province, so we can only imagine how much better the situation would be if Byzantine soldiers did not mutiny over lack of pay or if the local Berbers were not dissatisfied with Justinian's settlement. Likewise for Italy, since the imposition of eastern bureaucracy annoyed local elites (who had profited from serving the highly Romanised regime of the Ostrogoths) and the deposition of two popes had upset many western Christians. This wouldn't be a problem if the new regime had not needed the support of both local elites and the Church to effectively govern the province as empire's strength waned in the late sixth century; Justinian's less than perfect record in Italy was therefore I think a major cause of the endless Italian revolts of the seventh century.

As it was, the western provinces were still beneficial to the east, since North Africa and Sicily were economically very useful (particularly after the loss of the even wealthier Egypt and the Levant) and the prestige was obviously great, but these gains could have been made all the greater if Justinian and his officials ruled more wisely or if his ambitions were more realistic. This is of course all hypothetical, but I think it is true enough that Justinian's conquests were a mixed bag in terms of their effects.