According to When is the katakana form of wo (ヲ) used?, を is almost always used only for the particle, and is usually pronounced o (お).
There are some dialects where を is pronounced with a "w", but the same is true for the obsolete kana ゐ and ゑ:
Because the pronunciation was lost. "Wi" and "we" are still in some dialects, but standard Japanese does not have those sounds. These characters were just spelling. Similarly in English, we pronounce "through" as "thru" because the "gh" sound is long gone. [emphasis added]
Why was を spared even though ゐ and ゑ have been deemed obsolete? Was changing the writing of the object marker particle seen as too radical a change? Or is を pronounced "wo" more widely than ゐ and ゑ are pronounced as "wi" and "we"?
As @ZhenLin said in the comments, there are three particles left unchanged in the reform of the usage of kana: は へ を.
They are left unchanged because they are so widely used, and changing them would result in too much in the writing form. I quote from a book*(I don't know the book, so the contents are in fact from wiki):
*現代かなづかいの精神・抜粋（国語シリーズ8／文部省著、統計出版・昭和27年3月）
The spirit of the modern Kana usage (an extract) (Japanese Language Series 8, By the Ministry of Education, Culture, Sports, Science and Technology)
「本を読む」のををば、をと書く例外をことわっている。これが問題である。なぜこんな例外を許したか。例外にせずに、これも「お」と書いたらよいではないか、という非難がごうごうと聞える。これには、こういう理由がある。
もちろん例外は、よくよくでないかぎりは設けないほうがよい。委員会でもそれは皆心得ていたことなのである。だから、この例外を設けたのは、よくよくのことなのである。
およそ改革は、ことに万人の所有である言語の改革は、まさつの少ない、万人のすぐついてこられるものでなければ、案がいかにりっぱでも、机上の理想論に終って、実現ができない。理想としては、だれもだれも助詞のををもおにしてしまいたい。しかし、助詞というもの、ことに「が」「の」「に」「を」「へ」「は」などは、最もたくさん出てくる。〔中略〕いちいち
これわ それわ わたくしわ
それお これお わたくしお
これえ それえ わたくしえ
というように書くようになると、あまりにも、今までと変りすぎて異様さが目だち、ちょっと実行の手がにぶる。この助詞さえ、もし今までどおりにして置いてよかったら、他の点は、漢字で書くとほとんど隠れて、新かなづかいも、大部分今までどおりで済む〔中略〕助詞だけは漢字で書けず、いつもかなであって、必ずひっかかる、いちいち直すにかかる手もうるさいが、見る目にも抵抗が多過ぎて、すぐ実行できるか、あやぶまれる。これが、大新聞社側の決定的な意見であった〔中略〕いかにも、「わ」「お」「え」が、目にたって、一見異様であって親しめなかった記憶が、ある委員たちにもあったのである。
大事の前の小事である。実行できない案では、いかに美しくってもなんにもならない。要は実行できる案でなければ、一時強行されても、少しでも無理があると、動天返しになる憂いがある。
そこで委員会も、助詞を元どおりにのこすという妥協案を決定するよりほかにしかたがなかったようである。
"There is exceptions that を in 本を読む would be written as を. This is a problem. Why the exceptions are permitted? Why not write this as お and elimination all exceptions? Often there are criticisms about this. There is the following reason for this. Of course exceptions should not be allowed unless it can be avoided. The committee is well aware of that. However, these exceptions are the ones that cannot be avoided.
"Reform, especially the reform of language that is used be everybody, unless it can be followed by everybody in a short time, it will only be an ideal plan on the desk, and cannot become true. As an ideal (plan), everybody wanted change the particle を to お. However, the particle, especially 「が」「の」「に」「を」「へ」「は」 are most widely used. If we change them all, and write as
これわ それわ わたくしわ
それお これお わたくしお
これえ それえ わたくしえ
there would be too much change from the original writing, and would be hard to be put into practice. If only these particles are written as the original, other changes will mostly be hidden when kanji is used. The new kana usage will not have too much change in actual writing. (...) Only the particles won't be written in kanji, and are always written in kana, so will certainly be affected (by the reform). Changing all of them will cause too much effort, and it will cause too much resistance from people who read it. This is the decisive comment from the big publishing companies. (...) some members of the committee also (think) that 「わ」「お」「え」will stand out in the text, and make the text not look like normal Japanese.
"This is a 'little thing' before a big reform. A plan that cannot be put into practice will be nothing however good it is. If it is not a practical plan, even it is forced into use, it maybe reversed as long as there are something (unreasonable).
"Thus, the committee has to use the plan that keeps all the particles."
You should see that を is only kept as a particle, its appearances in other words are all changed to お, just like ゐ and ゑ changed to い and え.
