No, I don't think you're argumentative, and I like the question!

Yes, I do feel that having too many open credit cards with a bank will hurt your likelihood of getting approved for future cards with that bank. That's because the banks exposure to you is already large, and they may not want the additional lending risk.

I also close accounts if the retention bonus doesn't cover the annual fee. So if I get 2,000 AA miles for not closing my AA account, but have to pay an annual fee of $85, I will close the account.

That results in a lot fewer open cards than I would otherwise have.

Here's my experience so far:

Chase - I haven't been allowed to have more than 5 cards with them. Since most of their reward cards have an annual fee, I either keep the card for ~10 months and then cancel, or I cancel when I am denied another Chase card and want to get approved.

I don't ride very hard with Chase (perhaps 4 new cards a year) because they are cracking down on frequent applications! My last chat with a chase lending analyst was more like an inquisition, but I did get the card approved.

Citibank - Their retention bonuses are weak and I usually wait until the bonus hits my account and then cancel the card. This automatically limits the number of open accounts. I think I've had 6 open accounts with them at one time.

Bank of America - 2 of my oldest cards are with BOA, as are some of the newer cards. I have 4 open BOA cards and still get approved for cards. Of course, there will be a limit, but I'm trying to see what that limit is for me.

American Express - I haven't got more than 2 cards with them at any time.

As others have suggested, this is not an exact science. Most results will vary from individual to individual, and you have to determine what level of risk is agreeable to you.
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Million Mile Secrets Big Travel. Small Money.