Well, I think that depends on your style of play.
That being said, most of said items can (and should be!) procured out of thin air (probably by spending Momentum, cf. p. 183 ff. of the Core Rulebook). That’s how the system’s written to work. Characters on screen in Star Trek possess the items they need, if the plot commands they have access to it and lack them, if the plot commands they don’t.
Starfleet medical personnel can, under normal circumstances (including away missions), always access a standard medkit (cf. pages 196, 183 of the Core Rulebook).
Regarding the rest of your Equipment packs: If you plan on giving them out to every away team as a standard regardless per mission – I’d say your group is right, that’s not very true to on-screen Star Trek.
If you, in contrast, just want to declare that you, in a circumstance you would need one of said items, want to obtain it out of said packs – well, no problem in the stricter sense.
Yet, I, personally, would say: No need to bother!
If you’re on a mission with a shuttle, just equip yourself out of the shuttle’s storage and/or with the shuttle’s replicator. No need to pre-define what’s in the shuttle, that’s what Opportunity Cost is for (if needed, if you’ve got the time, all of these items will be free to procure on a standard shuttle under normal circumstances).
If you’re on a standard away team mission, just have someone beam down equipment you need. The smaller items might just be conveniently stowed in one of your pockets (I’m looking at the gloves, the flashlight or the knife).
If you’re on an away mission where you will be on your own for a certain amount of time, you will probably have some bagpacks. Again, no need to pre-define whats in said bagpacks, that’s what Opportunity Cost is for (if you aren’t considered to simply bring an item if it’s reasonable you brought it).
Star Trek Adventures is not written to be a Zombie Survival Game where planning and resource-management is a crucial part of the game. In the series, Starfleet personnel most of the time has access to the items they need and it’s part of a plot, if they don’t. Rules on equipment and obtaining items reflect that. If it’s reasonable you can just grab an item you need (such as a weapon, conveniently hidden under your console), simply do so (and maybe pay Opportunity and/or Escalation cost). If simply grabbing the item would be a bit far-fetched, you would need to create an opportunity to acquire these items, first. If it’s reasonable you can acquire the item with a bit of work/improvisation, it should be no problem. 2 Momentum for the opportunity, plus Opportunity and maybe escalation cost. Don’t bother with the contents of your away team equipment pack. If you need any one of these items or something not included in your list, simply declare it’s part of the standard away team equipment pack. If all agree it’s reasonable that there is such an item in the shuttle/bagpack the away team brought – fine, you now have it and can proceed with the Drama STA is written to be revolving around.