UPDATE March-2020: The chrome://flags
option listed below in my original answer no longer works as the flags appear to have been removed from the UI (although for some time after they were visibly removed from the UI, the options did still appear to persist if you had previously disabled these features in the UI - although this is no longer the case).
However, as stated in comments by @RIanGillis you can still disable these options on the Chrome shortcut / command line by adding the --disable-features
argument. For example:
.../chrome.exe --disable-features=OmniboxUIExperimentHideSteadyStateUrlTrivialSubdomains,OmniboxUIExperimentHideSteadyStateUrlScheme,OmniboxUIExperimentHideFileUrlScheme
This appears to restore the original functionality for me (tested Chrome v80.0.3987.132). http://
is still hidden (and shows "Not secure" instead). https://
is shown as are www
subdomains.
Another option, as stated in @wOxxOm's answer below, appears to be to install Google's Suspicious Site Reporter extension which also gets the protocol and subdomains back.
ORIGINAL ANSWER (No longer works):
The behaviour you are seeing is consistent with having the "Omnibox UI Hide Steady-State URL Scheme and Trivial Subdomains" setting enabled within chrome://flags
.

Returning this flag to "Default" (or "Disabled") and restarting the browser (prompted) should get your scheme + subdomains back. This is on Chrome Version 67.0.3396.87 (Official Build) (64-bit) - Windows.
Except checking that setting does not show "Enabled"; rather it shows "Default".
As far as I can gather, whether "Default" means "Enabled" or "Disabled" is built-in to the Chrome executable. So, this is primarily version dependent. Note also that settings vary between "Developer" and "Stable" builds.
Settings can also be enabled/disabled in command line switches. So this is another area that is worth checking. Reference: https://peter.sh/experiments/chromium-command-line-switches/ - although I don't see much relating to the Omnibox in this list.
UPDATE Sept-2018: As noted in another answer, from Chrome Version 69 (tested Version 69.0.3497.81), this feature now seems to be enabled by "Default". So, you must explicitly set this to "Disabled" to remove this feature.
UPDATE Aug-2019: This option/flag has since been split into two (possibly since version 72 - according to @Kyborek in comments):
- Omnibox UI Hide Steady-State URL Scheme
- Omnibox UI Hide Steady-State URL Trivial Subdomains
The "Default" setting is enabled, so these options must be explicitly set to "Disabled" to get the "Scheme" and "Trivial Subdomains" back in the URL address bar. (Note that the insecure "http" scheme/protocol is always hidden, regardless of this option.)

There is also a new(?), rather ominous, option: "Omnibox UI Hide Steady-State URL Path, Query, and Ref" which currently (Chrome version 76) appears to be disabled in its "Default" state. Something to keep an eye on though!

UPDATE Nov-2019: Unfortunately, it seems that since version 78 these flags have now been completely removed from the UI.
However, whilst these flags appear to have been removed in the UI, if you have previously disabled these flags in an earlier version then the options appear to stick and the "trivial subdomains" and "(HTTPS) URL scheme" remain visible.