Were the apostles “expert” witnesses?
If I understand the thrust of the question correctly, you are asking how the apostles expected their testimony in the gospels to be received - but in the process you appear (perhaps unintentionally) to be conflating the original audience and modern readers into a single group.
I would prefer to delineate those who read the gospels into at least two, and probably several more groups, and indeed the different gospels may even have been written with different audiences in mind. Luke at least seems to be primarily addressing a converted reader:
1:1Inasmuch as many have undertaken to compile a narrative of the things that have been accomplished among us, 2just as those who from the beginning were eyewitnesses and ministers of the word have delivered them to us, 3it seemed good to me also, having followed all things closely for some time past, to write an orderly account for you, most excellent Theophilus, 4that you may have certainty concerning the things you have been taught. ESV
From the perspective of 'Theophilus', it seems likely that Luke was regarded as an 'expert' - and he may well have taken on trust things he wrote whereas a man encountering Luke's gospel today for the first time might
- have preconceived animosity towards religion
- have a sensible policy of not believing things just because someone wrote them
- have already put their trust in some other person or faith than the one Luke holds
, to name but a few possibilities.
19:15“A single witness shall not suffice against a person for any crime or for any wrong in connection with any offense that he has committed. Only on the evidence of two witnesses or of three witnesses shall a charge be established. ESV
It seems reasonable not to expect someone who is not already a believer to accept the testimony of Luke alone - and indeed I find it very helpful that the we are surrounded by so great a cloud of witnesses from the varied Bible texts.
The remaining question then becomes whether Luke (or indeed God) intended his gospel to be a tool for convincing/persuading those who do not believe that it is a true account of the important facts about the life, death and resurrection of Jesus, as well as for building up 'Theophilus' (and perhaps other believers).
This goes to the heart of how a man is converted - is it the moment before he hears the gospel, so he can receive it, or the moment after, as he chooses to respond. In either event, at least for John, that intent is explicit:
20:31but these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name. ESV