@sudanglo

PMEG gives a definition

PMEG:
Aktiva participo prezentas agon aŭ staton kiel priskribon de ĝia subjekto:

ANT dum la ago – la ago ankoraŭ ne finiĝis
INT post la ago – la ago jam finiĝis
ONT antaŭ la ago – la ago ankoraŭ ne komenciĝis

with examples
 

• Viro, kiu ankoraŭ legas, estas leganta viro.
  
• Viro, kiu antaŭe legis, estas leginta viro.
  
• Viro, kiu poste legos, estas legonta viro.

Noteworthy in the definition is the word priskribo, i.e. the compound verbs in Esperanto do not denote an action as such but describes a state. This becomes even more apparent with the passive forms.

In the chapter for compound verbs PMEG states

PMEG:
La kunmetitaj ANT-formoj tre malofte estas bezonataj. Ili emfaze montras, ke io estas daŭra, kiam io alia okazas.

In this example of "In three years, I will have been living here for a decade" we have exactly this situation: passes three years and at the end of that time period the living still happens.

Usually you want to avoid complex verb forms, but I agree that estos loĝanta is a more elegant solution here than a rewording. And I think why. If you compare the sentences

● In three years, I will have been living here for a decade.

and

● By tomorrow, I will have finished writing my letter.

a crusial difference is that living is a long-lasting action while finishing is a short one. Therefore estos loĝanta but kompletigos sound the most elegant translations.

'estos loĝanta' in English would be 'will/shall be living'.

'This time next year I shall be living in Australia'. This tells us nothing about the length of the period up to the point of migration.

However, for 'I will have been living here for 10 years' to be true, it must also be true that for the 10 years up to the relevant time, this is where I have been residing - as does estos loĝinta ĉi tie jam dek jarojn.

Whether I might move elsewhere is not relevant. You might use estos loĝinta in circumstances where you intend to move elsewhere, but equally if you intend to stay put.

You are just reflecting on how long your residency will have been at some time in the future .

The chapter 28.1. Participoj kiel A-vortoj in PMEG gives the definition I mentioned above. Down in that chapter is a paragraph titled La vokaloj de la participoj, where it is said

PMEG:
AS montras ĉefe nuntempecon de la ago, dum ANT kaj AT montras daŭrecon aŭ ripetadon de la ago.

and

PMEG:
INT kaj IT montras, ke la ago plenumiĝis, eventuale antaŭ alia ago.

Now the definition says that we are dealing with a description, of an action. What does that mean? It means that
 

• estis + participo describes the state of an action in the past
  
• estas + participo describes the state of an action in the present
  
• estos + participo describes the state of an action in the future

The time of the participle is in relation to the time of the verb esti, meaning that
 

• -inta/ita shows that the action in a finished state
  
• -anta/ata shows that the action in a continuing state
  
• -onta/ota shows that the action in a future, not-yet-have-begun state

Think about time in the original phrase "In three years, I will have been living here for a decade". Here we are describing the state of an action in the future, thus estos, and at that particular time the action, living, is in a continuing state, i.e. it has begun sometime before we are describing it and it still continues at the time of description, thus loĝanta.

Should you say loĝinta, it would mean that the living-action is already over, but that does not make sense here.

This "rigidness" with time is the most important reason why it is often much easier just to use the simple verb forms.

PS. As you can see there are 3x3 compound verb form both for active and passive voice in Esperanto. Luckily most are not used.

"In three years, I will have been living here for a decade"

Kiel facila estas la Germana:

"In drei Jahren wohne ich hier schon ein Jahrzehnt."

Simple "loĝas". Sed, ĉar oni ne povas vidi la estontencon, kaj ĉar ne estas certeco pri estonta loĝloko, oni dirus germane:

"Ich wohne hier schon sieben Jahre."

There ae suprising few hits in the Tekstaro for esti + aktiva participo. But here's one, Metsis, with loĝinta that certainly does not imply cessation of residency. That is your point, isn't it, that loĝinta implies necessarily no longer living there.

PLURAJ eŭropaj ŝtatoj praktikas formojn de nacia prefero, tiel nomatajn “simpligita civitanigo”. Konforme al interkonsento subskribita en 1969, Islando, Svedujo, Danlando, Norvegujo kaj Finnlando establis inter si escepto-sistemon. Tiel, finnlanda enmigranto devas esti loĝinta nur du jarojn en Danlando por rajti ricevi ties civitanecon, kontraŭ sep jaroj por la aliaj eksterlandanoj.

What would be the point of granting Danish citizenship to persons leaving the country?