I don't think the 4th line should be playing more minutes. That's not what's going to help them. It may help them in the sense that the 4th line will be better, but that won't win them many more games, if any. The top 9 NEEDS to be better and NEEDS to be the ones carrying this team. They're the ones whose play will lead to more wins.
That's why I think the constant talk about the 4th liners on the team is overblown.
When you have a fourth line that can take defensive zone draws, that's fewer defensive zone draws your better players have to take.
When you have a fourth line that ends most of their shifts in the offensive zone, that's more offensive zone starts for your better players.
When you have a fourth line that can't play anything more than a heavily-sheltered, extremely limited role, that's taking offensive zone draws from your best players, and it's also not really giving them the breather they could really use.
When your top players are playing a ton of minutes there's a bigger chance they'll putter out in a crucial moment. We've seen this a few times this year where the team's best players just look plain exhausted. That happens when they have to play too many minutes, and it happens when they have a lot of d-zone starts where they have to skate the puck end-to-end on a regular basis before they can even start creating a scoring chance.
To say a decent fourth line doesn't matter, is, with all due respect, short-sighted. An improvement to the fourth line doesn't make a world of difference, but it makes things easier for the rest of the lineup. And it's also easier to improve your fourth line than it is to try and make some big trade for your top nine that'll likely leave another gaping hole somewhere else.
You can keep saying that the top nine need to carry the team, and you'd be right. The fourth liners' role is to make that carrying a little easier.