The reason the Tetrarchy is 'highly regarded' is primarily due to what it achieved. Due to the lack of any contemporary history of the Tetrarchy, the way it has been judged it by seeing how the Roman Empire was when the Tetrarchy began, and how the Tetrarchs left it when they left/abdicated/were killed. Doing this shows us that the Empire was close to collapse when the Tetrarchy was formed, but following its collapse everything the Empire was rejuvenated with a new life; economically, politically, and militarily. With this said, there is a debate that similarly due to a lack of evidence, the Tetrarchy has been given mistakenly high praise. I will explain the reasons for this alongside my answer.
When we look at the conditions preceding the Tetrarchy, we see that Diocletian (the 'First Tetrarch') entered a world which was on the verge of breaking point; the frontiers were far from safe, coinage had been heavily debased, and local administrations across the Empire were failing in their duties. On a basic level, the Tetrarchy is highly regarded because it did something successfully unique. There had been multiple emperors before, but Diocletian was able to create a system with four emperors to immense success; they could each led their own army to protect the borders, but their loyalties were guaranteed by the hierarchal system of Tetrarchy politics. As well as this, Diocletian was able to serve as the senior Tetrarch all the while allowing the others to govern their seperate territories. However, this is also an example of how the Tetrarchy's praise has been too high. Diocletian did not aim to bring the Empire under four emperors, he was forced to by the spiraling military situation. He reacted well and opportunistically to fix things in the short term, but this presented other issues which would become clear upon his abdication. What you must remember with Diocletian is that everything he did was done militarily, including his approaches to economic and religious policy. So, what did the Tetrarchy actually do to change things? I will offer two examples of how the Tetrarchy was ambitiously successful, while at the same time making great errors which set them on a path for failure.
Firstly, the Tetrarchy was presented with a broken currency. Diocletian scrapped the coinage and utilised the annona. This was a system of trading with like-for-like goods, which was even used to pay taxes. Diocletian's use of such a system shows his willingness to innovate. Diocletian also had more mints opened and brought in new coins (which were, sadly, restricted to use within the army). However, this innovation did not always work to his favour. By 301, the economic reforms already put in place (earlier Currency Decree and use of annona) were not working as well as Diocletian had thought, so he introduced the Edict of Maximal Prices. This was supposed to be an empire-wide order which listed the maximum price which all goods could be sold for in an attempt to solve a worsening inflation. It was, again, innovative, ambitious, and well-intended. However, this edict fell flat and was quickly repealed. The main issue was that there was no way of realistically enforcing such an order across the empire. Diocletian, being the military whiz, decided the best way to enforce it was through capital punishment, but there is no evidence of anyone being killed for disobeying the Prices Edict. Though Tetrarchic economic policy is a bit of a roller coaster, the period that followed under Constantine was a rich one, so we must assume that at least part of what Diocletian did was successful, even if the Prices Edict was a massive failure.
Secondly, the Tetrarchy made attempts to reform local government. Before Diocletian, local administrations were run by decuriones, curiales, and curators. The former two were local individuals (wealthy landowners) who would collect taxes and oversee building work and the daily workings of towns and cities. The latter position was an imperial official who could carry out the emperor's policy in local towns. These positions were all unpaid, but there was an assumption that they would skim off from local taxes as a sort of wage. Diocletian knew this sort of corruption was making the economic situation worse, to he made attempts to stamp out corruption. This would seem like a good idea, but it only made things even worse. People no longer wanted to volunteer for these positions, and so Diocletian again approached it militarily. As Roger Rees explains, he conscripted people to take up these roles on pain of losing their properties. This may have worked, but certainly brought resentment to Diocletian, especially from landowners in Egypt. As well as this, we can observe that his changed to local government might have failed completely, because during the Great Persecution no one wanted to follow his edicts against the Christians. However, by Constantine's reign, local governance was once again flourishing, so can we attribute its later success with the systems put in place by the Tetrarchy? It is hard to say. There was definitely a positive change after the period of rule under the Tetrarchy, so perhaps Diocletian's hardline approach was actually rather more successful than we would be led to believe.
To conclude with my two examples then, the Tetrarchy has been rightly well regarded in its ending of the third-century crisis. It solved problems of military, political and economic uncertainties, and bolstered the power of the emperor to pave the way for future leaders like Constantine (who, after all, grew up under the Tetrarchy and may have taken inspiration from it). However, recent scholarship has focused on a more balanced approach, which acknowledges the Tetrarchy's incredible successes, but does not neglect its failures - of which it had many. You are right to question why the Tetrarchy has been viewed so highly, but you must remain aware of how it fundamentally changed the Roman world with vast reforms (both successful and unsuccessful) which set in motion the beginning of the period of Late Antiquity. Additionally, the collapse of the Tetrarchy system can be attributed to the absence of Diocletian, who was able to single-handedly hold everything together, and so although successful, the Tetrarchy was not able to continue without his presence - which must have been powerful and overbearing, for he personally held together the four pillars of Tetrarchic control.
Ancient:
Eusebius, Ecclesiastical History, tr. H.J. Lawlor (London, 1927).
Modern:
Corcoran, S. (1996), ‘Empire of the Tetrarchs’ (Oxford).
Lucas, C. (1940), ‘Notes on the Curatores rei Publicae of Roman Africa’, The Journal of Roman Studies, Vol. 30.
Rees, R. (2004), ‘Diocletian and the Tetrarchy’ (Edinburgh).