This is not true.  The ATO - for instance - serves all of their statutory demands by mail to the address on record with ASIC, as do many businesses which issue statutory demands on a regular basis.  This is one reason why not keeping your details current on the ASIC registers is potentially catastrophic.  It's also why it's a good idea to list your lawyer or accountant's office for service of notices because statutory demands are not issued through courts and many people ignore them assuming that they're just a letter of demand because they don't realise their significance.

Where issuing a statutory demand through a lawyer can be tricky is the requirement that the affidavit be sworn by someone who has personal knowledge of the circumstances of the debt -this is obviously somewhat more difficult if the lawyer cannot get the client into their office to swear the affidavit as any deficiency in the affidavit will make render the statutory demand invalid.

Caveats are messy and easily set aside unless you have a true "interest in land".  The onus is on the caveator to prove that such an interest exists and that the caveat is being used for a proper purpose.  Trying to obtain a caveat in relation to the personal property of a company director in regard to a company debt which has not been proven (as opposed to an interest held by a mortgagor, a spouse, a joint property owner, a property purchaser, etc) is asking for the caveat to be set aside with an award of costs against the person who sought it.