I don't think that materially really had anything to do with it.
Sprint was dying - with extraordinarily high debt, in 2007, well before Softbank bought them, and indeed they lost money every year from 2008 forward - https://www.statista.com/statistics/481739/sprint-corporatio...
The Merger with Nextel managed to kill what was great about Nextel, and what was good about Sprint, and they lost customers in droves (mostly former Nextel ones). In reality Sprint bought Nextel's OAM equipment and their customers, and moved all the legacy Sprint customers onto the surviving billing and network management platforms (Nextel). The iDEN turndown also lost even more customers, most of whom who realized they didnt need PTToC after all (which is too bad, because on dedicated CDMA hardware, it worked really great).
Then they needed to start rolling out LTE (Network Vision) - and NV didnt start in earnest until 2012/13 - and as someone who was on the field end of it, was very very very poorly managed. Sprint some years prior had outsourced all their engineering expertise to Ericsson, which means they had no one in house with any knowledge. They only realized that 18 months in, and then scrambled to get people back from Ericsson (who I will note, they did not contract any of the deployment management to).
I only know this because I was in the middle of the deployment as a field resource in Seattle.
My guess is only half the sites in the network (in Seattle Market) had enough customers to pay their fixed costs.
I concluded while I worked there that there was no way for four carriers to be viable, there isnt enough spectrum allocated, and you pay the same fixed costs over and over again.
I'll go further, Sprint had a massive switch facility for the LD operations with room for like 4 DMS250's in Tacoma, but that's not where they put the SPCS 5ESS, that was in Kirkland in a rented building (and interestingly enough, it's still part of T-Mobiles operations today), there was also another Motorola iDEN switch also in Kirkland.
Post merger they never really made any effort to reduce their fixed costs (sites, switching centers, et al), because that would have cost money - they also got bled dry by having to foot the entire bill for rebanding the SMR band, which was on the order of 2.5 billion dollars. They did close stores (and RS was a major outlet for Sprint Sales, before it went belly up) which contributed to problems later.
So I don't know where you got your info, but I think its hooey - before Softbank bought Sprint, they didn't have the capital to upgrade their 2G/3G network to LTE, much less consider a merger with T-Mobile.