I dont see the problem. Joomla 3.8 ships with version 3.6.2 and anyone updating to 3.8 or installing 3.8 will get that version. The standalone version is only needed when we need to update the component outside of a regular joomla update for technical reasons

For reference the version number for core xml is updated automatically whenever the bump script is run

It is not a problem but this does not means it is right.
The last version of Joomla! Update IS 3.6.1 and not 3.6.2.

yes, it is not a big problem. But now we try to write the new documentation about how to update from Joomla 3.4 or 3.5 and we need to specify to update (manualy) before the com Joomla! Update to the last version 3.6.1, because no auto update are available for com Joomla! Update and if no at the latest version the update procedure is wrong.
But after the update to Joomla 3.8 the com Joomla! Update is at the 3.6.2 version.

because no auto update are available for com Joomla! Update

Strange as I got the option to update the component

in Joomla 3.4 ?

I am double checking now. But I definitely had it the other day when doing an upgrade

I got the option to update the component only in Joomla 3.6.0
for the <targetplatform name="joomla" version="3.6"/> in the XML ?
http://update.joomla.org/core/extensions/com_joomlaupdate.xml

for me is better:
<targetplatform name="joomla" version="3.[456]" />

Sorry I should have had more coffee.

I think you have just identified why the upgrades from old versions are failing.

We limit the upgrade to 3.5.1 and from there it goes directly to the latest version which as you have identified means that it misses 3.6.0 and the update to com_joomlaupdate

The change you mentions above should resolve that I think
@mbabker @zero-24

I'm going to review that update thing when i got back to home so we can propose a fix. (#18012)

@AlexRed @zero-24 Please see this old issue joomla/update.joomla.org#41 and a article I Referenced in the issue description.

That update component is obsolet please take a look into #18192 thanks. As this update path is not longer needed i'm going to close here. Thanks.