A few points to make regarding the above. One of the first is that 8-16 VLS cells is not really a corvette-type system, such a loadout is more typically found aboard frigates. Relating to that, one of the major drivers of the cost of a warship is the systems fitted, as opposed to the overall size, hence the adage that, "steel is cheap and air is free..." IIRC additional weapons systems, and more advanced weapons systems, sensors and shipboard electronics, can often be a third to half the cost of acquisition. To provide perhaps another perspective on this, Israel's
Sa'ar 6-class corvette, itself based upon the German MEKO 100 patrol corvette has an estimated cost of ~USD480 mil. per vessel according to
Naval Technology, with an overall length of 90m and displacement of ~2,000 tons.
The planned Type 31 frigates for the RN are estimated to cost ~USD$514 mil. (USD$2.57 bil. for five vessels, again per
Naval Technology) with an overall length of ~139m and displacement of ~5,700 tons or more.
The weapons systems are somewhat different, with the Israeli corvette having a larger gun (76 mm vs. 57 mm), but one is also talking about a difference in cost of ~USD$35 mil. per vessel, with the more expensive vessel having nearly three times the displacement whilst being fitted with overall comparable systems. One major difference is that the larger Type 31 frigates are going to have more room and potential displacement for future growth and upgrades, as well as the potential for significantly greater range (~7,500 n miles vs. 2,500 miles).
The basic gist of what I am trying to illustrate is that it gets difficult and especially expensive, to try and cram highly capable systems into smaller sized hulls, to the point that there is very little if any cost savings upfront. Long-term, smaller hulls which are intended to be highly capable likely end up becoming more expensive, because of the costs and difficulties associated with managing weight and displacement issues as upgrade programmes are done to keep a vessel and systems relevant.
Now I cannot speak knowledgeably about the actual shipbuilding process (there are others here on DT who can) but I would imagine that the steel-bashing part of constructing a smaller vessel/hull would be faster than a larger vessel, but that difference might not be all that significant. However, fitting out a vessel with all the systems required to make it useful and usable, this includes all internal wiring, cabling, and piping, as well as the installation of all shipboard systems like machinery, gen sets, sensors, weapons, electronics and CMS, etc. then one could very well find that installing everything required into a smaller hull takes just as long, since there is less space available to get everything fitted.
Now one area which has been repeatedly mentioned is that most corvettes, at least those fitted with comprehensive weapon and sensor/CMS packages, tend to be rather limited in terms of range and/or endurance. Others might still persist in disagreeing, but from my POV this is a critical issue for Australia. To once again provide some context, once of the potential transit routes that a RAN vessel sailing between Singapore and Darwin might take is ~3,600 km or just under 2,000 n miles. A corvette transiting this SLOC would likely find itself on a one-way trip absent being able to stop and refuel and re-provision en route or get RAS whilst underway. A larger vessel like a frigate with fuel of perhaps 6,000 n miles and a 21 or 28 day endurance would likely be able to make a round trip transit if need be. As an additional aside, the larger frigate might also be able to operate with a higher cruising speed which would shorten the time required for the transit, thus eating less into the mission endurance. Using the German
Braunschweig-class corvette as an example, they are listed with a range of ~4,000 n miles at 15 kts, but cruising at that speed it would take ~5.5 days to complete a one-way transit whilst the corvette only has an endurance of seven days without a tender.