A few half-truths being propagated here. The decline in cross-city services, whether suburb to suburb or simply terminating on the far side of the city centre to provide maximum passenger convenience, is a process that's been going on for decades. There have also been various different factors affecting that process.
Immediately prior to deregulation genuine cross-city services ran Whitefield-East Didsbury and Chorlton-Moston. A number of Hyde Road services terminated at Victoria Railway Station, most Wilmslow Road services circled the city centre, and some services from Salford via Chapel Street went through to Piccadilly Gardens (primarily from Swinton and the Eccles Old Road corridor). Other Salford services terminated at the Arndale Bus Station or Victoria Bus Station (different location to the rail station). The latter, though slightly remote from the heart of the city, did have a convenient layover area under the arches at nearby Greengate.
Deregulation saw Victoria Bus Station closed to reduce PTE costs and concerns about congestion saw the end of cross-city services and far fewer services terminating on the far side of the city centre. This put a lot of pressure on both Piccadilly and Arndale Bus Stations. At the same time the rapid rise of new operators led to an increase in the numbers of elderly buses in the city and so began Manchester City Council's long-term bias against buses especially once Metrolink was approved: clean electric trams = good, noisy smelly diesel buses = bad. The one outlier was the introduction of services 90/790 linking Rossendale to Manchester which went to Chorlton Street Coach Station, mimicking the long established Ribble X43 Timesaver from Burnley (forerunner to today's Witchway service).
In due course Metrolink opened but at the cost of reducing the size of Piccadilly Bus Station. Traffic Regulation Orders were also brought in to prevent buses parking up all over the place and forced operators to adopt schedules which were unreliable. The big bang, literally, was the bomb of 1996 which not only led to the closure of Arndale Bus Station but also the loss of Cannon Street as a convenient north-south route across the city. It is little wonder that so many operators were in turmoil during this period!
Eventually Shudehill Interchange was built and though it provides much needed terminal capacity in reality it is just a sticking plaster of a solution. The ideal solution which has been staring everyone in the face is to completely pave over Piccadilly Gardens to create room for a decent size central bus station. But despite frequent outbreaks of ASB it seems that Mancunians are loathe to give up the open space even though as a whole Manchester has a large number of parks and other green spaces
The alternative may well be for Bee Network to re-introduce numbers of cross-city services with sufficient vehicles allocated to provide genuine resilience and slightly extended layovers at the outer termini. Perhaps the restraining factor is London's experience with such services which have been cut back considerably over the years/decades. Nevertheless the existence today of routes like the 41, 50 and Vantage services does demonstrate what can be done. And the gradual improvement in bus emissions, even if it had to be spurred on by bringing in the LEZ, ought to make buses running across the heart of the city an easier sell.