Many still spend vast sums on fundraising even with healthy recurring donations - it just means they spend more on prime-time TV advertisements. Charities should not be trying to sell their services along side perfumes, car insurance and supermarket advertisements - single-use "things" - they should be going for the long term organic growth by fostering a great reputation for efficiency ("good done" per unit currency).
People selling perfume and car insurance clearly believe that prime-time advertising is cost-effective. Why shouldn't charities use the same media?
If I give $1 to a charity, I'm more than happy for them to spend it on fundraising if they're getting $1.05 ROI. That's a fantastically effective use of my money, as long as the $1.05 gets used effectively to deliver on their charitable purpose.
There's probably a good game-theoretic argument against fundraising activity if charitable donations are zero-sum, but I've yet to see any evidence that they are.
They also have to repeatedly spend money on fundraising. Monthly donations are good for charities, just like monthly subscriptions are good for software businesses - they have a very high LTV if churn is properly controlled and make the finances of the organisation far more predictable.