Well, the reasons you cited for not liking to sing in church are valid. You feel self conscious or that you "aren't good enough" (voice is robotic, etc.). But you aren't singing for the congregation, you are singing for God.
Psalms 100:1 "Make a joyful noise unto the LORD, all ye lands."
Nowhere in the Bible does it say that you have to have a good voice (if it did, that would exclude A LOT of people). It doesn't say that you have to have expressive or emotional inflection or tones (that would exclude many of us Aspies). It just says "make a joyful noise."
I worried about singing in church because I was afraid I didn't sound "right." Now, I close my eyes to block out everyone and sing from my heart. I don't know if I sound "robotic" but I listen to the words and mean each and every word I sing - I am singing to God.
Paul had some things to say about singing in church:
Ephesians 5:18-20 - And do not get drunk with wine, for that is dissipation, but be filled with the Spirit, speaking to one another in psalms and hymns and spiritual songs, singing and making melody with your heart to the Lord; always giving thanks for all things in the name of our Lord Jesus Christ to God, even the Father.
Colossians 3:16-17 - Let the word of Christ richly dwell within you, with all wisdom teaching and admonishing one another with psalms and hymns and spiritual songs, singing with thankfulness in your hearts to God. And whatever you do in word or deed, do all in the name of the Lord Jesus, giving thanks through Him to God the Father.
Singing (in church) is to be the overflowing of Christ as He dwells in you, your spirit. It is the manifestation of the Word of Christ taking root within you.
It also sets the tone, the atmosphere and prepares the heart for receiving God's Word through the lesson or sermon.
Singing in church (or worship and praise songs even when you are not at church) is important because it infuses your spirit with God's Word and His will for you. It keeps the channels open for you to more easily receive Him, His direction for you, if that makes sense.
Please, don't worry about what others think of you. God thinks your voice and way you sing is BEAUTIFUL! He things YOU are BEAUTIFUL just the way you are. He wants to hear you worship Him.
Besides, you may think that you sound mechanical, but that might not be true. Satan delights in deceiving us and stopping us from pursuing our relationship with Christ, keeping us from truly realizing just how much He loves and accepts us as we are. Satan wants to keep us from worshipping, praising and relying on God for our needs. He will lie to you to try to make you doubt God's love for you and try to separate you from God. Don't let him!
I hope that answered your question. Feel free to message me privately if you are more comfortable with that.