Should add in the plethora of back-to-back Tests as another thing that makes it implausible currently.
And I highly doubt more than the odd game every 3 or 4 years would take a week to complete in this country. Look at the number of games which have been significantly interrupted by weather and have still clearly had loads of overs to go to complete a result in recent years. These are the Test draws in England since 1998:
The Oval, India, 2007: 441 overs bowled (just 9 lost), no result forthcoming anyway.
Lord's, India, 2007: just 1 more wicket needed, would have been a handful of overs.
Lord's, WI, 2007: 347 overs bowled (103 lost), would have been another day-and-a-bit and possibly a result forthcoming.
Lord's, Pakistan, 2006: 436 overs bowled (just 14 lost), no result forthcoming anyway.
Lord's, Sri Lanka, 2006: 398 overs bowled (42 lost), would have had a result anyway but for stupid numbers of dropped catches, but would have been a couple of extra sessions and it'd have been one anyway.
The Oval, Australia, 2005: 305 overs bowled (145 lost), would probably have been another day and a bit or so to get a result, but it was a September Test anyway which is something I'd avoid along with back-to-back matches.
Old Trafford, Australia, 2005: just 1 more wicket needed, would have been a handful of overs.
Edgbaston, South Africa, 2003: 328 overs bowled (122 lost), would probably have been less than a day to get a result.
The Oval, India, 2002: 354 overs bowled (96 lost), last day washed-out, no result in the offing anyway, but an extra day could have been played.
Trent Bridge, India, 2002: 361 overs bowled (89 lost), wouldn't have been more than another session and a bit to get a result.
Lord's, Sri Lanka, 2002: no overs lost, legit draw.
Old Trafford, West Indies, 2000: 357 overs bowled (93 lost), another day might possibly have produced a result.
Trent Bridge, Zimbabwe, 2000: 298 overs bowled (152 lost), but a result would probably have taken just another day-and-a-bit (given play was lost on all 5 days and 2 sessions wouldn't have been enough).
Old Trafford, New Zealand, 1999: 337 overs bowled (113 lost), a result would have been unlikely to have taken more than another day.
Old Trafford, South Africa, 1998: 453 overs bowled (more than the stipulated minimum
), legit draw. Though only 1 wicket standing - thrilling game.
Edgbaston, South Africa, 1998: 344 overs bowled (106 lost), last day washed-out, would probably have had a result within a day.
Look back further and the story is much the same. Only 2 or 3 times per decade would games go on for an eternity. And I think this'd be worth it - as the above shows, it'd result in the draw becoming a rare thing.