"Yes, "successors" naturally means someone who comes AFTER the Apostles - following in their footsteps and given the power to continue to lead the Church on earth. It is safe to assume that the original Apostles are long gone and in heaven by now."
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I'm glad we can agree on something, that there are no Apostles living today.
The second part of your statement though gives me pause. There is no SCRIPTURAL basis for your assertion that the men who followed the Apostles were granted any supernatural powers. For example after Mathias was appointed to replace Judas we never heard from him again.
First, you seem to believe that the Bible completely records EVERYTHING that was done by the early Church! The Bible is a compiliation of SOME of the Apostles' letters to individual churches that asked for THEIR help and guidance on particular issues. It is not a systematic theology book or a catechism. Thus, we shouldn't expect the Bible to discuss EVERY Apostle's work. At any rate, we can find more information outside of the Inspired Holy Writ that is ALSO reliable.
And even within Scriptures, in particular, the Pastorals and the Acts of the Apostles, we see the conferment of power being given by the "Church elders" to others, such as Timothy and Titus. This "laying of hands" was understood as the giving of the Spirit in a special way, a vocation and a sending - thus, in a sense, making these second generation Christians "apostles" in that they were sent to continue spreading the Word of God. Do you think that Mat 28:20 was meant only for THAT generation of men and women? God's Word transcends time and place.
Regards