Tendering individual trades by architects: expensive?

The documents are of course prepared by the architect. But as nordanney wrote: being active yourself doesn’t hurt either.

Requesting an excessive number of bidders can indeed be harmful: competitors are not enemies, you know each other and talk to one another. If an architect, together with their client, requests an excessive number of bidders overall, they notice that. This causes the architect to fall into the category of "we only answer their tenders if we have too little to do" – and consequently, from then on, they really have to request nine bidders to get five responses. Meanwhile, five offers for a roof are already one (for hip roofs, even two) too many. Anyone who shoots the shot as well as the scattergun in tenders will soon have a problem with their reputation as a reliable partner.

Requests = call to check if there is interest/capacity. That automatically reduces the number. That's what it's about. Because some already decline. And five offers for a roof, I personally did not find too many for our region (Berlin Brandenburg). In any case better than just 1 or none.

Would you also obtain quotes from general contractors in parallel?

Yes, it's worth it. But only if you find someone who offers you a fixed price without a risk of price increases.

And I personally did not find five offers for a roof to be too many for our region (Berlin Brandenburg).

The purpose of the offers is not (and should also not have the side effect!) to give the bidders extra work. Therefore, their number should be appropriate. That means they should be in proportion to the price and performance differences that are approximately to be expected. This means: more where there is more volume of offers; and also more where, although there is less volume, the execution involves more complexity (more expensive tiles, control instead of mere switches and sockets, hip roof on angle instead of gable roof on rectangle, basically overall something special instead of run-of-the-mill). And yes, in border regions near foreign countries, naturally one more offer than in the interior of the country. But always with moderation and not as occupational therapy – the effort of a qualified offer also deserves a fair chance of winning the contract. So in Brandenburg, I agree with you, at least for a hip roof an exceptional five offers for the roof, yes, but not also nine inquiries (something is wrong there). In case of doubt, better to "call in" additional bidders if too few have responded (which usually has reasons that one can also influence) than to send out (too) many inquiries from the start.

A craftsman once said I don't make money by writing quotes

[A craftsperson once said: I don't make money by writing quotes]

He probably didn't understand it and/or simply can't do it any better.