Is there any benefit to purposefully losing attacks? For example, I've been trying to get more resources with the Barch army, but I've noticed I haven't been doing so well recently. Maybe it's because the higher the trophy count, the harder the bases you attack are, so could it be a solution to throw some attacks and just drop a single barbarian, then end the game?
Since the treasury is the best protected resource when your base is raided, I always try to get 5 stars so loot is added to it. This does seem to increase my trophy count, even when I'm trying to focus on resources.
Best Answer
TL;DR
Yes it is a valid technique to use, even after the 5 star loot bonus update. To lose trophies, if you have a hero, drop the hero and quit instantly, that way you don't have to remake a barbarian each time; otherwise, just dropping a barb is a good way to do it. If your hero isn't hurt he will be back for the next raid without any down time.
Longer Explanation
Purposefully losing trophies is a valid technique and should be employed in certain situations. Since higher level bases and more serious players tend to have more trophies, losing trophies will help you encounter more casual players. Especially if you are using a weak army like barch and having difficulty, it may be a good idea.
You are also correct that since the addition of the 5 star bonus, and bonuses being made larger in the recent update, it is less appealing to lose trophies; nevertheless it can still be quite a good strategy. One real world example is that now I'm a TH9 around 3000+ trophies, at this level I see mostly TH10s while 'nexting' that I don't want to attack, and the TH9s I do see have maxed bases, higher heroes, good layouts, and usually don't have much loot. On my friends account, he stays at 2600 trophies and the attackers and defenders are much weaker, and it is generally easier to find a base to attack, however, he does not receive the higher star bonus and raid loot bonus, so it's a trade off.
To find a good trophy count may take some trial and error, as it will vary with your town hall, troop and hero upgrades. Also, these trophy counts will change over time as the player pool naturally will shift a little bit up or down, so don't expect to stay at one range forever. Supercell will inevitably release more patches changing farming and matchmaking that will alter trophy counts as well, so keep on eye on updates!
To lose trophies, if you have a hero, drop the hero and quit instantly, that way you don't have to remake a barbarian each time; otherwise, just dropping a barb is a good way to do it. If your hero isn't hurt he will be back for the next raid without any down time.