While there are benefits to traveling to manchester airport to get a flight to heathrow for onward connections (itinerary protected from manchester for example), the downsides often outweigh them.
If you're flying from anywhere other than terminal 5, you have to get a bus transfer and go through security again. Total time from wheels up at Manchester to wheels up at Heathrow other than T5 is at least 160 minutes. While I've done taxi to gate in under 5 minutes at T3, I'd give it at least 30 minutes before wheels up, putting a MAN arrival to LHR departure time for T5 at at least 2h40 (30 minutes at MAN, 70 in the air, 60 Minimum Connection Time T5).
For any other terminal it's 3h10 from MAN arrival, and having to go through security twice and a bus. And Manchester isn't great, they've been de-premiuming for a while now, I'd far rather go through the dedicated checkin/security/lounge at T5 than fight through Manchester, get a plan, face a bus gate, then a walk from the north side of T5 to the south to get to the lounge.
However that's the MCT. Experience in my itinerarys typically means a 2-2.5 hour layover at Heathrow, so you're looking at least 3h30 from MAN arrival to LHR departure.
With HS2 it's 50 minutes from MAN arrival to OOC, 15 minute wait for a Hex, 15 minutes to T5, so 1h20, then an hour for leisurely security etc. Throw in 30 minutes padding, you're looking at MAN arrival to T5 departure in under 2 hours. I'd go for a 1400 train from Airport to get a 1600 flight. Others who are more paranoid with security might go for a 1300 train for a 1600 flight.
That's a 1600 flight from any of the terminals though, not just T5.
To get a 1600 flight from Heathrow now you'd have to get a 1350 flight from Manchester, meaning arriving at Manchester at 1320, an extra 40 minutes.
On the way back I can be from enterring passport control and out of heathrow in 10 minutes tops. 10 minute wait for the express, 15 to OOC, so 35 minutes. Average 10 minute wait for a train to Manchester is 45 minutes, and at airport station 95 minutes from landing.
There's no way the plane can compete with that. Even with perfect connections it would take 130 minutes from LHR arrival time to Airport arrival time.
These times are massively stacked in favour of the airport too -- the assume a taxi arrival/departure rather than public transport, they also assume that the nearest HS2 station is airport (if you're nearer Crewe or Picadilly then the savings are even bigger)
The only benefit of flying from Manchester is that your itinerary is protected, as long as you arrive at the airport about 50 minutes before travel. If your flight is cancelled or delayed, the airline has to cover you under EU261, put you on the next flight, put you in a hotel, compensate you, etc.
With HS2 that protection doesn't apply until you arrive at heathrow, but that's not enough to keep Birmingham-London flights going.