Postgresql – Why does postgres choose to sort instead of scanning the index

I have the following table:

# \d service
       Table "public.service"
   Column    |   Type   | Modifiers 
-------------+----------+-----------
 customer_id | integer  | not null
 date        | date     | not null
 service     | smallint | not null
 has         | boolean  | 
Indexes:
    "service_customer_id_idx" btree (customer_id)

# select count(*) from service;
   count   
-----------
 327535416
(1 row)

Time: 75047.508 ms

# select version();
                                                   version                                                

-------------------------------------------------------------------------------------------------------------
 PostgreSQL 9.5.4 on x86_64-redhat-linux-gnu, compiled by gcc (GCC) 6.1.1 20160621 (Red Hat 6.1.1-3), 64-bit
(1 row)

I tried to come up with a query for which it is obviously beneficial to use the
index, since the results can be taken directly from the index in the correct
order:

# explain (analyze,verbose) select customer_id from service order by customer_id;
                                                               QUERY PLAN                                                               
----------------------------------------------------------------------------------------------------------------------------------------
 Sort  (cost=64804990.92..65623829.48 rows=327535424 width=4) (actual time=487209.250..546557.064 rows=327535416 loops=1)
   Output: customer_id
   Sort Key: service.customer_id
   Sort Method: external merge  Disk: 4482448kB
   ->  Seq Scan on public.service  (cost=0.00..5045816.24 rows=327535424 width=4) (actual time=2.705..49659.173 rows=327535416 loops=1)
         Output: customer_id
 Planning time: 0.093 ms
 Execution time: 554914.731 ms
(8 rows)

Time: 554919.649 ms

As you see, Postgres prefers to do a sequential scan and then sort the results.

Interestingly, if I add a limit clause, it does decide to use the index:

# explain (analyze,verbose) select customer_id from service order by customer_id limit 10;
                                                                             QUERY PLAN                                                                              
---------------------------------------------------------------------------------------------------------------------------------------------------------------------
 Limit  (cost=0.57..32.97 rows=10 width=4) (actual time=2.509..2.773 rows=10 loops=1)
   Output: customer_id
   ->  Index Only Scan using service_customer_id_idx on public.service  (cost=0.57..1061141647.19 rows=327535424 width=4) (actual time=2.503..2.760 rows=10 loops=1)
         Output: customer_id
         Heap Fetches: 10
 Planning time: 4.285 ms
 Execution time: 2.906 ms
(7 rows)

Time: 28.178 ms

Why does Postgres behave this way, and how could I debug this? Is there a way to
ask it to show alternative plans and their cost calculations?

Here's the execution with seqscan turned off:

# explain (analyze,verbose) select customer_id from service order by customer_id;
                                                                                QUERY PLAN                                                                                 
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 Index Only Scan using service_customer_id_idx on public.service  (cost=0.57..1061141647.19 rows=327535424 width=4) (actual time=2.753..346400.896 rows=327535416 loops=1)
   Output: customer_id
   Heap Fetches: 327535416
 Planning time: 1.921 ms
 Execution time: 355637.985 ms
(5 rows)

Time: 355647.367 ms