why Japanese says the following?
This is simply because we don't always need the nuance of "there is" or "there exists". This applies to all the four examples below.
Compare these more literal translations:
私はアレックスだ。 / I am Alex.
私はアレックスという名前がある。 / There is the name "Alex" of mine.; I have the name "Alex".
The latter sounds like the speaker is giving weight to his name rather than himself. Indeed, this Japanese sentence could imply that the speaker is proud of his name.
In fiction, we often see a character say 俺には○○という立派な名前がある after he is called お前 or そこの etc.
この料理はおいしい味がある。
This sounds unnatural, though おいしい味がする is fine. I'm not sure "This dish has a good taste" is common in English but it's not in Japanese.
This is because we are not interested in the existence of tastes but how good or bad it tastes.
プレゼントを買ってもらって、嬉しい感じがある。
I actually sometimes say ~感じがある on Twitter, but it's not at all formal writing. It sounds indirect.
彼は悪い態度がある。
We don't say this. As you mentioned, 態度が悪い is far better. Alternatively, 悪い態度が見られる is also OK. It has a little more objective sound.
Furthermore, are there alternatives for
- experience
- necessity
- tendency
- probability
without using ~がある?
experience: You can use 経験する (to experience), 以前(昔)~した (I did ~ before) etc. but I think ~がある is common.
For example:
オーストラリアへ旅行に行ったことがある。 == 昔オーストラリアへの旅行を経験した。
necessity: You have many options. 必要だ(na-adjective: necessary), ~しなければならない(have to), ~せざるを得ない(have no choice but to) etc.
さらに議論する必要がある。 == さらなる議論が必要だ。 == さらに議論しなければならない。
tendency: Choose appropriate ones: 傾向が見られる(tendency is observed), しがちだ(often do), よく~する(often do), ~タイプだ(slangy; mostly used for a person), 他と比べて~だ(more ... than others)
日本人は長時間働く傾向がある。 == 日本人は他と比べて長時間働く。
彼は感情が顔に出る傾向がある。 == 彼は感情が顔に出るタイプだ。
probability: There are variety of ways to mention probability. Care about the level of probability. ~かもしれない (equal meaning to 可能性がある; not mentioning the value of probability. less formal), ~可能性が考えられる, ~ないとも限らない, etc.
日本が優勝する可能性がある。 == 日本が優勝するかもしれない。
I noticed that noun + がある (where the noun is often 漢語) sounds more formal than others. So you might have read many formal pieces of writing but not so many informal or colloquial ones. If you turn your eyes to informal ones, you might find various new expressions.